Questions asked by Romilus L.

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• Find the value of c for which the area enclosed by the curves y=x^2-c^2 and y=c^2-x^2 is 576?
  
• A steady wind blows a kite due to west. The kite height above ground from horizontal position x=0 to x=25 given by y=50-0.1(x-15)^2. Find the distance travel by the kite?
  
• Find the arc length function for the curve y= integration 1 to x √(t^3-1)dt,1<x<4?
  
• Use cylindrical shell method to find the volume of the solid obtained by rotating the region bounded by the given curves x^2=y and y^2=x about y=-1?
  
• Use cylindrical shell method to find the volume of the solid obtained by rotating the region bounded by the given curves x^2=y and y^2=x about y=-1?
  
• Describe the solid whose volume is represented by #int_(0)^(3) (2pi x^5)dx#. ?
  
• Find the value of #lambda# such that the vectors #(1,3,5)#, #(2,-1,3)# and #(4, lambda, 1)# are linearly dependent.?
  
• A thin plate covers the triangular region bounded by the x-axis and , the line y=x and the x=1.?
  
• A thin plate covers the triangular region bounded by the x-axis and the lines x=1 and y=2x in the first quadrant. The plate density at the point (x,y) is rho (x,y) = 6x+6y+6. find the plates, mass, first moment, centre of mass about the coordinate axes.?
  
• Evaluate double integral #int int (1-x^2/a^2-y^2/b^2)dx dy # over the first quadrant of the ellipse #x^2/a^2+y^2/b^2 = 1#, by using the transformation #x=au# and #y=bv#?
  
• Find the point on the sphere x2 + y2 * z2 :4 which is farthest from the point (1, -1, 1),?
  
• The population of the town in three consecutive years are 5000 , 7000 and 8400 respectively. what will be the population of the town in the fourth consecutive year according to geometrical increase method? with the solution.?
  
• Find the value of the surface integral (2x^2yi - y^2j + 4xz^2k).dS where is S the surface of the cylinder y^2 + z^2 = 9 bounded by the planes x=0 and x=2?
  
• Evaluate double integration 0 to 8 and y^1/3 to 2 (e^x^4) dy dx. why do we need to change the variables in evaluating multiple integrals?