Integration: the Area Problem

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Questions

• How do you find the area of a region using integration?
• How do you use integration to find area under curve?
• Why does integration find the area under a curve?
• How do I evaluate #int_0^5|x-5|dx# by interpreting it in terms of areas?
• How do you find the area of the parallelogram with vertices (4,5), (9, 9), (13, 10), and (18, 14)?
• How do you evaluate the integral of absolute value of (x - 5) from 0 to 10 by finding area?
• How do you find the area of the parallelogram with vertices k(1,2,3), l(1,3,6), m(3,8,6), and n(3,7,3)?
• How do you find the area of the parallelogram with vertices: p(0,0,0), q(-5,0,4), r(-5,1,2), s(-10,1,6)?
• How do you evaluate #int5# between the interval [0,4]?
• What is a surface integral?
• What are examples of functions that cannot be integrated?
• How do you determine the values of the coefficients a and b that will give a minimum value of the area, #S#, of the region enclosed by the curve #y=-x^2+ax+b# (which passes through point (1,2)) and the curve #y=(1/2)x^2#?
• How do you find the area bounded by the curve #y= 3-2x-x^2# and the x axis?
• How do you find the region inside cardioid #r=1+cos(theta)# and outside the circle #r=3cos(theta)#?
• How do you find the region inside cardioid #r=(alpha)(1+sin(theta)), (alpha)>0#?
• How do you find the area of the region cut from the second quadrant by the cardioid r=1-cosθ?
• How do you find the area of the region enclosed by the cardioid #r=2+2cos(theta)#?
• How do you find the area inside of the Cardioid #r=3+2cos(theta)# for #0 <= (theta) <= 2pi#?
• How do you find the area inside of the Cardioid #r = 2+2cosθ# and outside the circle r = 3?
• How do you find the area inside of the circle #r = 3sin(theta)# and outside the cardioid #r = 1 + sin(theta)#?
• How do you find region bounded by circle r = 3cosΘ and the cardioid r = 1 + cosΘ?
• How do you find the area bounded by the cardioid #r=1+cos(theta)#?
• How do you find the area of the region shared by the circles #r=2cos(theta)# and #r=2sin(theta)#?
• How do you find the area of the region shared by the cardioid #r=2(1+cos(theta)) #and the circle r=2?
• What is the area under the curve in the interval [-3, 3] for the function #f(x)=x^3-9x^2#?
• What is the area under the curve in the interval [0, 3] for the function #y=x^2+1#?
• What is the area under the curve in the interval [2,7] for the function #1/(1 + x^2)^(1/2) #?
• What is the area under the curve #y = 2x^{-3}# from 6 to 10?
• What is the area under the curve #f(x)=x^2+2# from 1 to 3?
• What is the area under the curve #y=sqrtt# from 0 to 1?
• The area under the curve y=e^-x between x=0 and x=1 is rotated about the x axis find the volume?
• How do you find the area of the region under the given curve y = (2x + 2)^1/2 on the interval [0,1]?
• How do you use integrals to find the area bounded by the curve y = (x^2 - 9) and the x-axis for x = 0 to x = 5?
• How do you find the area #y = f(x) = 4/x^2# , from 1 to 2 using ten approximating rectangles of equal widths and right endpoints?
• Question #8e5b5
• How do you find the integral of #int dx/(sqrt(2x-1)# from 1/2 to 2?
• How do you find the area between the given curve #y= x^2# and the x-axis given in the interval [0,1]?
• How do you find the area between the given curve #y= x^(1/2)# and the x-axis given in the interval [2,5]?
• How do you find the area enclosed by the x-axis and the given curve #y=(6/x)# for x between -4 & -2?
• What is the area under #f(x)=x^3-1# in #x in[0,1] #?
• What is the area under #f(x)=x^2-3x+5# in #x in[0,1] #?
• What is the area under #f(x)=5# in #x in[0,2] #?
• What is the area under #f(x)=5x-1# in #x in[0,2] #?
• What is the net area between #f(x)=sinx# in #x in[0,2pi] # and the x-axis?
• What is the net area between #f(x)=tanx# in #x in[0,pi/3] # and the x-axis?
• What is the net area between #f(x)=ln(2/x)# in #x in[1,2] # and the x-axis?
• What is the net area between #f(x)=ln(x+1)# in #x in[1,2] # and the x-axis?
• What is the net area between #f(x)=x/ln(x^2)# in #x in[3,10] # and the x-axis?
• What is the net area between #f(x)=(x-x^2)/ln(x^2)# in #x in[1,2] # and the x-axis?
• What is the net area between #f(x)=(x-x^2)/ln(x^2+1)# in #x in[1,2] # and the x-axis?
• What is the net area between #f(x)=(x-3)e^x# in #x in[1,2] # and the x-axis?
• What is the net area between #f(x)=7x-8# in #x in[1,2] # and the x-axis?
• What is the net area between #f(x)=2/x-x# in #x in[1,2] # and the x-axis?
• What is the net area between #f(x)=ln(x^3-x+2)/x^2# in #x in[1,2] # and the x-axis?
• What is the net area between #f(x)=(x^2-5)/(x^3-5x# in #x in[1,2] # and the x-axis?
• What is the net area between #f(x)=xsinx# in #x in[0,4pi] # and the x-axis?
• What is the net area between #f(x)=sinxcosx# in #x in[0,2pi] # and the x-axis?
• What is the net area between #f(x)=x^3-x^2+5# in #x in[2,5] # and the x-axis?
• What is the net area between #f(x)=x^3+4x^2-2# in #x in[2,5] # and the x-axis?
• What is the net area between #f(x)=-4x^3+2x^2-5# in #x in[1,5] # and the x-axis?
• What is the net area between #f(x)=-x^3-2x^2-x# in #x in[0,3] # and the x-axis?
• There is a line through the origin that divides the region bounded by the parabola ?
• What is the net area between #f(x) = 3x^2-4x+2# and the x-axis over #x in [1, 3 ]#?
• What is the net area between #f(x) = 3x^2-x+2# and the x-axis over #x in [1, 3 ]#?
• What is the net area between #f(x) = 3x^2-x+2# and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = x^2-x+2# and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = e^(3x)-4x# and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = e^(3x)-2x+1# and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = e^(3-x)-2x+1# and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = e^(3-x)-2x+1# and the x-axis over #x in [0, 3 ]#?
• What is the net area between #f(x) = e^(3-2x)-2x+1# and the x-axis over #x in [0, 3 ]#?
• What is the net area between #f(x) = sinx# and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = sinx - cosx# and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = sinx - cos^2x# and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = cosx # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = cosxsinx # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = cosxsin^2x # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = cos^2xsin^2x # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = cos^2xsinx # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = cos2x-sinx # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = cos2x-xsinx # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = xsinx # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = x-cosx # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = x-sinx # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = x-sin^2x # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = x-4cos^2x # and the x-axis over #x in [0, 3pi ]#?
• What is the net area between #f(x) = cscx -xsinx# and the x-axis over #x in [pi/6, (5pi)/8 ]#?
• What is the net area between #f(x) = cscx -cosxsinx# and the x-axis over #x in [pi/6, (5pi)/8 ]#?
• What is the net area between #f(x) = cotxcscx -sinx# and the x-axis over #x in [pi/6, (5pi)/8 ]#?
• What is the net area between #f(x) = x-xsqrt(4x-3) # and the x-axis over #x in [1, 4 ]#?
• What is the net area between #f(x) = x-xsqrt(4x+1) # and the x-axis over #x in [1, 4 ]#?
• What is the net area between #f(x) = x-sqrt(x+1) # and the x-axis over #x in [1, 4 ]#?
• What is the net area between #f(x) = x/sqrt(x+1) # and the x-axis over #x in [1, 4 ]#?
• What is the net area between #f(x) = 1/sqrt(x+1) # and the x-axis over #x in [1, 4 ]#?
• What is the net area between #f(x) = -sqrt(x+1) # and the x-axis over #x in [1, 4 ]#?
• What is the net area between #f(x) = x^2-sqrt(x+1) # and the x-axis over #x in [1, 7 ]#?
• What is the net area between #f(x) = (x-2)^3 # and the x-axis over #x in [1, 5 ]#?
• What is the net area between #f(x) = xe^x-3x # and the x-axis over #x in [1, 5 ]#?
• What is the net area between #f(x) = 4/x # and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = 2/x^3 # and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = 2/(x+3) # and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = 2/(x+1)^2 # and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = x^2-ln(x^2+1) # and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = -ln(x^2+1) # and the x-axis over #x in [1, 2 ]#?
• What is the net area between #f(x) = -xln(x^2-1) # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = x^2-xln(x^2-1) # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = sqrt(x^2+2x+1) # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = 1/sqrt(x^2+2x+1) # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = sqrtx-x # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = sqrt(x+3)-x^3 # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = sqrt(x+3)-x^3+6x # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = x^3+6/x # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = x^2+1/x # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = x^2+1/x # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = xlnx-xe^x # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = e^(2x)-xe^x # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = x^2-x+8 # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = x+8 # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = x-4 # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = 2x-6 # and the x-axis over #x in [2, 4 ]#?
• What is the net area between #f(x) = 2x-5 # and the x-axis over #x in [2, 3 ]#?
• What is the net area between #f(x) = 3-xsqrt(x^2-1) # and the x-axis over #x in [2, 3 ]#?
• What is the net area between #f(x) = xsqrt(x^2-1) + 6# and the x-axis over #x in [2, 3 ]#?
• Let R be the region in the first quadrant bounded above by the graph of #y=(6x+4)^(1/2)# the line #y=2x# and the y axis, how do you find the area of region R?
• A rectangle has one corner in quadrant 1 on the graph of #y=16-x^2#, another at the origin, and the third on the positive y-axis, and the fourth on the positive x-axis. How do you express the area, A, of the rectangle as a function of x?
• What is the area of the region in the first quadrant by the graph of #y=e^(x/2)# and the line x=2?
• What is the area of the region in the first quadrant enclosed by the graphs of y = cosx, y= x, and the y -axis?
• What's the area of the first quadrant region bounded by the y-axis, the line #y=4-x # and the graph of #y=x-cosx#?
• Let R be the region in the first quadrant bounded by the graphs of #y=x^2#, #y=0#, and #x=2#, how do you find the area of R?
• Let R be the region in the first quadrant enclosed by the graphs of #y=e^(-x^2)#, #y=1-cosx#, and the y axis, how do you find the area of the region R?
• Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of #y=sin(x)# and #y=cos(x)#, how do you find the area of R?
• How do you find the area in the first quadrant between the graphs of #y^2=(x^3)/3# and #y^2=3x#?
• Let R be the region in the first quadrant enclosed by the graph of #y=2cosx#, the x-axis, and the y-axis, how do you find the area of the region R?
• Let R be the first quadrant region enclosed by the graph of #y= 2e^-x# and the line x=k, how od you find the area of R in terms of k?
• Let R be the region in the first quadrant that is enclosed by the graph of #y=tan x#, the x-axis, and the line x=pi/3, how do you find the area?
• What is the area of the region in the first quadrant that is enclosed by the graphs of #y=x^3+8# and #y=x+8#?
• Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of #y=4-x^2# and #y=1+2sinx#, how do you find the area?
• Let f and g be the functions given by #f(x)=e^x# and #g(x)=1/x#. What is the area of the region enclosed by the graphs of f and g between x=1 and x=2?
• How do you find the area of the region between the graphs of #y=x^2# and #y=-x# from x=0 to x=3?
• Let R be the region in the first quadrant bounded by the x-axis, the graph of #x=y^2+2#, and the line x=4. What is a the interval for the area of R?
• Let R be the region in the first and second quadrants bounded above by the graph of #y=20/(1+x^2)# and below by the horizontal line y=2, how do you find the area?
• Let R be the region in the first quadrant bounded by the graphs of #(x^2/ 9) + (y^2 /81)=1# and #3x+y=9#, how do you find the area?
• How do you find the area bounded by the curves #y = -4sin(x)# and #y = sin(2x)# over the closed interval from 0 to pi?
• How do you find the area under the graph of #f(x)=e^(-2lnx)# on the interval [1, 2]?
• How do you use the trapezoidal rule with n = 4 to approximate the area bounded by the curves #y = sin2x#, the lines x = 0, y = 0, and x = 1?
• How do you write the definite integral to find the smaller area cut from the circle #x^2 + y^2 = 25# by the line x = 3?
• How do you find the volume when the region bounded by y = x+3, y = 0, x = -3 and x = 3 is revolved around the x-axis?
• How do you find the area enclosed by the curve #y^2 = x(1 - x)#?
• Let f and g be the functions given by #f(x)=1+sin(2x)# and #g(x)=e^(x/2)#. Let R be the region in the first quadrant enclosed by the graphs of f and g. How do you find the area?
• How do you find the exact value of the area in the first quadrant enclosed by graph of y=sinx and y=cosx?
• How do you find the area of the region bounded by the given curves #y = 6x^2lnx # and #y = 24lnx#?
• Question #cb563
• Question #fce84
• How do you find the area enclosed by graphs of #y=sqrt [x]# and #y= x^3#?
• Let r be the region bounded by the graphs of #y= sqrt(x)# and #y=x/2#, how do you find the area of R?
• How do we find the area inside the cardioid #f(theta)=a(1+costheta)#?
• Question #c62e7
• Find b, c and d so that the quadrilateral is a parallelogram with area equal to 80 square units?
• Let R be a region in he first quadrant bounded above by #y=x+2# and below by #y=e^x#, how do you find the area of R?
• What is the area of the largest rectangle that can be inscribed under the graph of y=2 cos x for -π /2 ≤x ≤π /2?
• Question #ad67f
• Question #d9bfd
• Question #75f31
• What is the area between the line #y = x# and the curve #y = x^3#?
• Question #40f71
• How do you use the limit process to find the area of the region between the graph #y=-2x+3# and the x-axis over the interval [0,1]?
• How do you use the limit process to find the area of the region between the graph #y=x^2+2# and the x-axis over the interval [0,1]?
• How do you use the limit process to find the area of the region between the graph #y=x^2+1# and the x-axis over the interval [0,3]?
• How do you use the limit process to find the area of the region between the graph #y=16-x^2# and the x-axis over the interval [1,3]?
• How do you use the limit process to find the area of the region between the graph #y=1-x^3# and the x-axis over the interval [-1,1]?
• How do you use the limit process to find the area of the region between the graph #y=64-x^3# and the x-axis over the interval [1,4]?
• How do you use the limit process to find the area of the region between the graph #y=2x-x^3# and the x-axis over the interval [0,1]?
• How do you use the limit process to find the area of the region between the graph #y=x^2-x^3# and the x-axis over the interval [-1,0]?
• How do you use limits to find the area between the curve #y=x^2# and the x axis from [0,5]?
• How do you use limits to find the area between the curve #y=2x^3# and the x axis from [1,5]?
• How do you use limits to find the area between the curve #y=x^4# and the x axis from [0,5]?
• How do you use limits to find the area between the curve #y=x^2+6x# and the x axis from [0,4]?
• How do you use limits to find the area between the curve #y=x^2-x+1# and the x axis from [0,3]?
• How do you use limits to evaluate #int 8xdx# from [0,2]?
• How do you use limits to evaluate #int (x+2)dx# from [1,4]?
• How do you use limits to evaluate #int x^2dx# from [0,4]?
• How do you use limits to evaluate #int8x^3dx# from [3,5]?
• How do you use limits to evaluate #int(x^2+4x-2)dx# from [1,4]?
• How do you use limits to evaluate #int(x^5+x^2)dx# from [0,2]?
• What is the area below the curve #f(x)=x^3 -4x^2 +2x+ 8# and bounded by the y-axis, the x axis and x=3 expressed as an integral?
• Question #e8898
• How do you find the area of region bounded by the graphs of y +x= 6 and y +2x-3=0?
• How do you find the area of the region under the curve #y=4x^-2# from x=1, to #x=oo#?
• How do you find the area of the region under the curve #y=1/sqrt(2x-1)# from x=1/2, to x=1?
• Let #R# be the region in the first quadrant bounded by the #x# and #y# axis and the graphs of #f(x) = 9/25 x +b# and #y = f^-1 (x)#. If the area of #R# is 49, then the value of #b#, is ? A) #18/5# B) #22/5# C) #28/5# D) none
• Given #f(x)# is a polynomial function of #x#, satisfying #f(x)*f(y)= f(x) +f(y)+f(x y)-2# and that #f(2)=5#. Then #f(3)# is equal to? A) 10 B) 24 C) 15 D) none
• What is the area bounded by the curves? : # 4x + y^2 = 32 # and # x=y #
• How do you use integrals?
• Find the area bounded by # x = -y^2 # and # y = x+2# using a double integral?
• Find the surface area of a sphere of radius r?
• Alex and Veronica were discussing the definite integral #int_0^3 (x^2 − 1)dx#. Alex said it represented the total area bounded by #f(x) = x^2 - 1# and the #x#-axis , between #x = 0# and #x = 3#. Veronica said the total area was larger?
• How do i answer this? # int_2^4 \ (2x)/(x^2+1) # via a Riemann sum.
• Write the Riemann sum to find the area under the graph of the function #f(x) = x^2# from #x = 1# to #x = 5#?
• A firm manufacturing 2000 items.It estimated that the rate of change of production P with the respect to additional number of workers x is given by dP/dx=100-12x^.5.If the firm employees 25 more workers,then the new level of production of the items is?