length of a curve

Question

Find the length of the curve y=x^3/2 from the point (1,1) to the point (4,8).

Answer 1

the integrand that makes sense is √(1+(dy/dx)²)dx integrated with x limits 1 to 4

have √(1+(9/4)x)dx

integrated is

(4/9)(2/3)(1+(9/4)x)^3/2 computed at x=4 and subtracting computed at x=1