What is the arc length of #f(x)=x^2-3x+sqrtx# on #x in [1,4]#? Calculus Applications of Definite Integrals Determining the Length of a Curve 1 Answer Jim H Jan 26, 2018 About 8.111. Explanation: #int_a^b sqrt(1+(f'(x))^2) dx = int_1^4 sqrt(1+(2x-3+1/(2sqrtx))^2)# # ~~ 8.111# 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 1462 views around the world You can reuse this answer Creative Commons License