Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5 (16 − x^2)^1/2 , y = 0, x = 2, x = 3, about the x-axis

ediculeN

ediculeN

Answered question

2021-02-25

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y=5(16x2)12 , y = 0, x = 2, x = 3, about the x-axis

Answer & Explanation

diskusje5

diskusje5

Skilled2021-02-26Added 82 answers

We picture the calculation as adding the volumes of cylinders with a height of dx and a radius of y. The volumes of such cylinder is (y(x))2π dx .
Therefore, the volume is V=[2,3](y(x))2πdx=π[2,3]25(16x2)dx=π[2,3](40025x2)dx=π(400x(25/3)x3|2,3=π(((4003)(253)33)(4002)(253)23)=725π3

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