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Question

1- Find the exact length of the curve.

y = (x^ 3 /3) + (1/4x),    1 ≤ x2


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 = √(5x) ,    3x5


4-

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

y1 + ex ,    0 ≤ x1

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