Question

# 1- Find the exact length of the curve.

*y* = (*x^ 3 /3) + (*1/4*x)*, 1 ≤ *x* ≤ 2

2-Find the exact length of the curve.

*y* = ln(1 − *x^2)*, 0 ≤ *x* ≤ 1/8

3- Find the exact area of the surface obtained by rotating the curve about the *x*-axis.

*y* = √(5 − *x) *, 3 ≤ *x* ≤ 5

4-

Find the exact area of the surface obtained by rotating the curve about the *x*-axis.

*y* = √1 + *e*^{x }, 0 ≤ *x* ≤ 1