What is the integral of pi(8.4x-2x^2)^2 ?

The integral of pi(8.4x-2x^2)^2 is pi(23.52x^3-8.4x^4+0.8x^5)+C

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integral of pi(8.4x-2x^2)^2

\int π (8.4 x - 2 x^{2})^{2} d x

π (23.52 x^{3} - 8.4 x^{4} + 0.8 x^{5}) + C

Solution steps

\int π (8.4 x - 2 x^{2})^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int (8.4 x - 2 x^{2})^{2} d x

Expand

(8.4 x - 2 x^{2})^{2} : 70.56 x^{2} - 33.6 x^{3} + 4 x^{4}

= π \cdot \int 70.56 x^{2} - 33.6 x^{3} + 4 x^{4} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π (\int 70.56 x^{2} d x - \int 33.6 x^{3} d x + \int 4 x^{4} d x)

\int 70.56 x^{2} d x = 23.52 x^{3}

\int 33.6 x^{3} d x = 8.4 x^{4}

\int 4 x^{4} d x = \frac{4 x ^{5}}{5}

= π (23.52 x^{3} - 8.4 x^{4} + \frac{4 x ^{5}}{5})

Simplify

= π (23.52 x^{3} - 8.4 x^{4} + 0.8 x^{5})

Add a constant to the solution

= π (23.52 x^{3} - 8.4 x^{4} + 0.8 x^{5}) + C

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What is the integral of pi(8.4x-2x^2)^2 ?
The integral of pi(8.4x-2x^2)^2 is pi(23.52x^3-8.4x^4+0.8x^5)+C