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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 = x7,  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 = 4x5, 1x2.

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 + 6x3/2,    0 ≤ x ≤ 1

4- Find the exact length of the curve.

xy^ 4/8  + 1/4y2,   1 ≤ y ≤ 2

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