What is the volume of the solid generated by revolving the region under y = sqrt(x) from x = 0 to x = 4 about the x-axis?
Answer and explanation
Correct answer: A. 8 pi
- Step 1: Use the disk method: V = pi * integral from a to b of [f(x)]^2 dx.
- Step 2: V = pi integral from 0 to 4 of (sqrt(x))^2 dx = pi integral from 0 to 4 of x dx = pi [x^2 / 2] from 0 to 4 = pi (16 / 2) = 8 pi.
Answer
8 pi.
Why not the others: '4 pi' divides 16 by 4 instead of 2; '16 pi' forgets the 1/2 factor in x^2/2; '2 pi' integrates sqrt(x) directly without squaring.
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