What is volumeabout y=0,y=2x^2,y=12x-4x^2,[0,2] ?

The answer to volumeabout y=0,y=2x^2,y=12x-4x^2,[0,2] is (384pi)/5

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volumeabout y=0,y=2x^2,y=12x-4x^2,[0,2]

volume about

y = 0, y = 2 x^{2}, y = 12 x - 4 x^{2}, [0, 2]

\frac{384 π}{5}

Decimal Notation

241.27431 \dots

Solution steps

Apply the volume formula:

\int_{0}^{2} π 4 x^{4} - (- 4 x^{2} + 12 x)^{2} d x

Solve

\int_{0}^{2} π 4 x^{4} - (- 4 x^{2} + 12 x)^{2} d x : \frac{384 π}{5}

The volume for solid of revolution is:

= \frac{384 π}{5}

((6 x + 1) y^{2}) \frac{d y}{d x} + 3 x^{2} + 2 y^{3} = 0

x \to - 4 lim (0)

\int_{4}^{\infty} e^{3 x} d x

\int tan^{5} (x) sec^{10} (x) d x

\frac{d y}{d x} = \frac{e ^{3 x}}{y ^{6}}

What is volumeabout y=0,y=2x^2,y=12x-4x^2,[0,2] ?
The answer to volumeabout y=0,y=2x^2,y=12x-4x^2,[0,2] is (384pi)/5