What is volumeabout y=0,y=x^2,y=4x-x^2,[0,2] ?

The answer to volumeabout y=0,y=x^2,y=4x-x^2,[0,2] is (32pi)/3

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volumeabout y=0,y=x^2,y=4x-x^2,[0,2]

volume about

y = 0, y = x^{2}, y = 4 x - x^{2}, [0, 2]

\frac{32 π}{3}

Decimal Notation

33.51032 \dots

Solution steps

Apply the volume formula:

\int_{0}^{2} π x^{4} - (- x^{2} + 4 x)^{2} d x

Solve

\int_{0}^{2} π x^{4} - (- x^{2} + 4 x)^{2} d x : \frac{32 π}{3}

The volume for solid of revolution is:

= \frac{32 π}{3}

(1 + cos (t)) y^{^{'}} = (1 + e^{- y}) sin (t), y (0) = 0

(x^{2} + 5) (8 - x)

\int \frac{2 x}{1 + 4 x ^{2}} d x

\frac{6}{x ^{3}}

\int \frac{3 x ^{2}}{4 5 - x ^{3}} d x

What is volumeabout y=0,y=x^2,y=4x-x^2,[0,2] ?
The answer to volumeabout y=0,y=x^2,y=4x-x^2,[0,2] is (32pi)/3