What is the integral from 2 to 5 of pi(x^2-1/5 x^4) ?

The integral from 2 to 5 of pi(x^2-1/5 x^4) is -pi 2118/25

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integral from 2 to 5 of pi(x^2-1/5 x^4)

\int_{2}^{5} π (x^{2} - \frac{1}{5} x^{4}) d x

- π \frac{2118}{25}

Decimal

- 266.15572 \dots

Solution steps

\int_{2}^{5} π (x^{2} - \frac{1}{5} x^{4}) d x

Take the constant out:

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

= π \cdot \int_{2}^{5} x^{2} - \frac{1}{5} 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_{2}^{5} x^{2} d x - \int_{2}^{5} \frac{1}{5} x^{4} d x)

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} \frac{1}{5} x^{4} d x = \frac{3093}{25}

= π (39 - \frac{3093}{25})

Simplify

π (39 - \frac{3093}{25}) : - π \frac{2118}{25}

= - π \frac{2118}{25}

What is the integral from 2 to 5 of pi(x^2-1/5 x^4) ?
The integral from 2 to 5 of pi(x^2-1/5 x^4) is -pi 2118/25