Question

# 1- Set up, but do not evaluate, an integral for

the area of the surface obtained by rotating the curve about the *x*-axis and the *y*-axis.

*y* = *x*^{7}, 0 ≤ *x* ≤ 1

(a) about the *x*-axis

(b) about the *y*-axis

2- Use the arc length formula to find the length of the curve *y* = 4*x* − 5, −1 ≤ *x* ≤ 2.

Check your answer by noting that the curve is a line segment and calculating its length by the distance formula.

3- Find the exact length of the curve.

*y* = 1 + 6*x*^{3/2}, 0 ≤ *x* ≤ 1

4- Find the exact length of the curve.

*x* = *y^ 4/*8 + 1/4*y*^{2}, 1 ≤ *y* ≤ 2