Question

# 1- Find the exact area of the surface obtained

by rotating the curve about the *x*-axis.

*y* = *x^3 /2 *+ 1/ 6*x *, 1/2 ≤ *x* ≤ 1

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

*x* = 1/3 (*y*^{2} + 2)^{3/2}, 4 ≤ *y* ≤ 5

3- The given curve is rotated about the *y*-axis. Find the area of the resulting surface.

*y* = 1/3 *x*^{3/2}, 5 ≤ *x* ≤ 21

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