Determining the Length of a Parametric Curve (Parametric Form)

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Questions

• How do you find the arc length of a parametric curve?
• How do you find the length of the curve #x=1+3t^2#, #y=4+2t^3#, where #0<=t<=1# ?
• How do you find the length of the curve #x=e^t+e^-t#, #y=5-2t#, where #0<=t<=3# ?
• How do you find the length of the curve #x=t/(1+t)#, #y=ln(1+t)#, where #0<=t<=2# ?
• How do you find the length of the curve #x=3t-t^3#, #y=3t^2#, where #0<=t<=sqrt(3)# ?
• How do you determine the length of a parametric curve?
• How do you determine the length of #x=3t^2#, #y=t^3+4t# for t is between [0,2]?
• How do you determine the length of #x=2t^2#, #y=t^3+3t# for t is between [0,2]?
• What is the arc length of #r(t)=(t,t,t)# on #tin [1,2]#?
• What is the arc length of #r(t)=(te^(t^2),t^2e^t,1/t)# on #tin [1,ln2]#?
• What is the arc length of #r(t)=(t^2,2t,4-t)# on #tin [0,5]#?
• What is the arc length of the curve given by #r(t)= (1,t,t^2)# on # t in [0, 1]#?
• What is the arc length of the curve given by #r(t)= (1/t,1,t)# on # t in [0, 1]#?
• What is the arc length of the curve given by #r(t)= (ln(1/t),t^2,t)# on # t in [1, 10]#?
• What is the arc length of the curve given by #r(t)= (e^-t,e^t,1)# on # t in [1, 2]#?
• What is the arc length of the curve given by #r(t)= (-t,2t^2,-t^3)# on # t in [3,4]#?
• What is the arc length of the curve given by #r(t)= (9sqrt(2),e^(9t),e^(-9t))# on # t in [3,4]#?
• What is the arc length of the curve given by #r(t)= (e^tsqrt(2t),e^t,e^(-2t))# on # t in [3,4]#?
• What is the arclength of #(sint/(t+cos2t),cost/(2t))# on #t in [pi/12,pi/3]#?
• What is the arclength of #(tant-sect*csct)# on #t in [pi/8,pi/3]#?
• What is the arclength of #(tant,sect*csct)# on #t in [pi/8,pi/3]#?
• What is the arclength of #(t-e^(2t),lnt)# on #t in [1,12]#?
• What is the arclength of #(t^2-t,t^2-1)# on #t in [-1,1]#?
• What is the arclength of #(t,t-1)# on #t in [-7,1]#?
• What is the arclength of #(3t^2,t^4-t)# on #t in [-4,1]#?
• What is the arclength of #(2t^2-t,t^4-t)# on #t in [-4,1]#?
• What is the arclength of #(2t^3-t^2+1,2t^2-t+4)# on #t in [-2,1]#?
• What is the arclength of #(9t^3-2t^2+15,-2t^2-12t-1)# on #t in [-2,3]#?
• What is the arclength of #(sqrt(t+2),1/t)# on #t in [1,3]#?
• What is the arclength of #(sqrt(3t-2),1/sqrt(t+3))# on #t in [1,3]#?
• What is the arclength of #(t/(5-t),8/t)# on #t in [1,4]#?
• What is the arclength of #(t/(1+t)^2,-1/t)# on #t in [2,4]#?
• What is the arclength of #(e^(2t)-t,t-t/e^(t-1))# on #t in [-1,1]#?
• What is the arclength of #(e^(-2t)-t^2,t-t/e^(t-1))# on #t in [-1,1]#?
• What is the arclength of #(t/(t+5),t)# on #t in [-1,1]#?
• What is the arclength of #(t-t^3,t+1)# on #t in [-2,4]#?
• What is the arclength of #(t-2t^3,4t+1)# on #t in [-2,4]#?
• What is the arclength of #(sqrtt,1/sqrt(t^2+3))# on #t in [1,2]#?
• What is the arclength of #(1/t^2,1/t)# on #t in [1,2]#?
• What is the arclength of #(1/(1-e^t),2t)# on #t in [2,4]#?
• What is the arclength of #(1/(t+te^t),-t)# on #t in [3,4]#?
• What is the arclength of #(t-3,t^2)# on #t in [1,2]#?
• What is the arclength of #(t-3t^2,t^2-t)# on #t in [1,2]#?
• What is the arclength of #(lnt/t,lnt)# on #t in [1,2]#?
• What is the arclength of #(t^2lnt,t-lnt)# on #t in [1,2]#?
• What is the arclength of #(t^2lnt,(lnt)^2)# on #t in [1,2]#?
• What is the arclength of #(t^2lnt,lnt^2)# on #t in [1,2]#?
• What is the arclength of #(t^2-lnt,lnt)# on #t in [1,2]#?
• What is the arclength of #(ln(t+3),lnt/t)# on #t in [1,2]#?
• What is the arclength of #((e^tlnt)/t,t/(e^tlnt))# on #t in [2,4]#?
• What is the arclength of #(t-3,t+4)# on #t in [2,4]#?
• What is the arclength of #(t^2-t-1,9t^2-2/t)# on #t in [1,4]#?
• What is the arclength of #(t-1,t/(t+5))# on #t in [-1,1]#?
• What is the arclength of #(sqrt(e^(t^2)/(e^t)+1),t^3)# on #t in [-1,1]#?
• What is the arclength of #f(t) = (t-e^(t),t-2/t+3)# on #t in [1,2]#?
• What is the arclength of #f(t) = (t,t,t)# on #t in [1,3]#?
• What is the arclength of #f(t) = (t^3-t^2+5t,9t)# on #t in [1,4]#?
• What is the arclength of #f(t) = (-2(t+3)^3,(t-2)^2)# on #t in [1,2]#?
• What is the arclength of #f(t) = (-(t+3)^2,3t-4)# on #t in [0,1]#?
• What is the arclength of #f(t) = (t-2,1/(t-2))# on #t in [0,1]#?
• What is the arclength of #f(t) = (tlnt,t/lnt)# on #t in [1,e]#?
• What is the arclength of #f(t) = (t+sqrt(lnt),t-sqrtlnt))# on #t in [1,e]#?
• What is the arclength of #f(t) = (tsqrt(lnt),t^3/(4-t))# on #t in [1,e]#?
• What is the arclength of #f(t) = (lnt/t,ln(t+2))# on #t in [1,e]#?
• What is the arclength of #f(t) = (sqrt(t-2),t^2)# on #t in [2,3]#?
• What is the arclength of #f(t) = (t^2sqrt(t-1),t^2+t-1)# on #t in [2,3]#?
• What is the arclength of #f(t) = (t-sqrt(t-1),t^2/(t^2-1))# on #t in [2,3]#?
• What is the arclength of #f(t) = (t-tsqrt(t-1),t/(t^2-1))# on #t in [2,3]#?
• What is the arclength of #f(t) = (t/sqrt(t-1),t/(t^2-1))# on #t in [2,3]#?
• What is the arclength of #f(t) = (t^3-1,t^2-1)# on #t in [2,3]#?
• What is the arclength of #f(t) = (t^3-t+55,t^2-1)# on #t in [2,3]#?
• What is the arclength of #f(t) = (te^(2t)-e^t-3t,-2t^2)# on #t in [1,3]#?
• What is the arclength of #f(t) = (e^(t)-e^(t^2)/t,t^2-1)# on #t in [1,3]#?
• What is the arclength of #f(t) = (t-7,t+7)# on #t in [1,3]#?
• What is the arclength of #f(t) = (t^2-5,e^t)# on #t in [1,3]#?
• What is the arclength of #f(t) = (t^3-t^2+t,t-t^2)# on #t in [0,1]#?
• What is the arclength of #f(t) = (sqrt(t^2-2t+1),t^2-2t+1)# on #t in [0,1]#?
• What is the arclength of #f(t) = (sqrt(t^2-t^3),t^3-t^2)# on #t in [-1,1]#?
• What is the arclength of #f(t) = (t-sqrt(t^2+2),t+te^(t-2))# on #t in [-1,1]#?
• What is the arclength of #f(t) = (t/sqrt(t^2+2),t/e^(t-2))# on #t in [-1,1]#?
• What is the arclength of #f(t) = (sint*cos2t,sint)# on #t in [-pi,0]#?
• What is the arclength of #f(t) = (sin^2t-cos2t,t/pi)# on #t in [-pi/4,pi/4]#?
• What is the arclength of #f(t) = (sin^2t/sin(2t),tant-sec^2t)# on #t in [pi/12,pi/4]#?
• What is the arclength of #f(t) = (cos2t-sin2t,tan^2t)# on #t in [pi/12,(5pi)/12]#?
• What is the arclength of #f(t) = (sin2t-tcsct,t^2-1)# on #t in [pi/12,(5pi)/12]#?
• What is the arc length of #f(t)=(3t-4,t^3-2t) # over #t in [-1,2]#?
• What is the arc length of #f(t)=(t^2-4t,5-1/t) # over #t in [3,4] #?
• What is the arc length of #f(t)=(t^2-4t,5-t) # over #t in [3,4] #?
• What is the arc length of #f(t)=(lnt,5-lnt) # over #t in [3,4] #?
• What is the arc length of #f(t)=(ln(1/t) ,5-lnt) # over #t in [3,4] #?
• What is the arc length of #f(t)=((4-t^2)e^t,te^t) # over #t in [3,4] #?
• What is the arc length of #f(t)=(3te^t,t-e^t) # over #t in [2,4]#?
• What is the arc length of #f(t)=(sqrt(t-1),2-8t) # over #t in [1,3]#?
• What is the arc length of #f(t)=(1/sqrt(t+t^2),2-8t) # over #t in [1,3]#?
• What is the arc length of #f(t)=(t-tsqrt(t-1),8-2t) # over #t in [1,4]#?
• Consider the parametric equation #x= 10(cost+tsint)# and #y= 10(sint-tcost)#, What is the length of the curve from #0# to #((3pi)/2)#?
• Question #89633
• Find the exact length of the curve (parametrics)?
• Parametric arc length?
• Find arc length given #x=t\sint#, #y=t\cost# and #0\let\le1#?