How do you find the arc length of the curve #y=xsinx# over the interval [0,pi]? Calculus Applications of Definite Integrals Determining the Length of a Curve 1 Answer Jim H Mar 21, 2018 Find #int_0^pi sqrt(1+(dy/dx)^2) dx# Explanation: #dy/dx = sinx+xcosx#, so we need #int_0^pi sqrt(1+(sinx+xcosx)^2) dx# which is about #5.04# Answer link Related questions How do you find the arc length of #y=ln(cos(x))# on the interval #[pi/6,pi/4]#? What is arc length parametrization? How do you find the length of a curve defined parametrically? How do you find the length of a curve using integration? How do you find the length of a curve in calculus? How do you find the arc length of #x=2/3(y-1)^(3/2)# between #1<=y<=4#? How do you find the length of the curve #y=x^5/6+1/(10x^3)# between #1<=x<=2# ? How do you find the length of the curve #y=e^x# between #0<=x<=1# ? How do I find the arc length of the curve #y=ln(sec x)# from #(0,0)# to #(pi/ 4, ln(2)/2)#? How do I find the arc length of the curve #y=ln(cos(x))# over the interval #[0,π/4]#? See all questions in Determining the Length of a Curve Impact of this question 4178 views around the world You can reuse this answer Creative Commons License