Question

Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, y = 4x; about the y-axis v = incorrect: your answer is incorrect.

Answer 1

The correct answer for  the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, y = 4x is 128/3 * π.

Volume of Solid of Revolution by Shell method is given by

V = 2π * integrate x(height) dx Here, height = 4x-x2

(1)& x-varies from x = 0 to x = 4 then from eqn(1)  V = 2π * integrate x(4x - x ^ 2) dx from x = 0 to 4 = 2π * integrate (4x ^ 2 - x ^ 3) dx from x = 0 to 4

Basic Rule(1) ∫ x^n dx =x^ n+1/ n+1

V=2 π [4((x ^ 3)/3) - (x ^ 4)/4] 0 ^ 4 =2 π[ 4/3 x^ 3 - x^ 4/4 ] 0 ^ 4

V = 2π [4/3 * 4 ^ 3 - (4 ^ 4)/4} - 0]

V = 128/3 * π.

Learn more about area under curve here :-

brainly.com/question/15122151

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