What is the integral from 0 to 1 of pi(5x^2)^2 ?

The integral from 0 to 1 of pi(5x^2)^2 is 5pi

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integral from 0 to 1 of pi(5x^2)^2

\int_{0}^{1} π (5 x^{2})^{2} d x

5 π

Decimal Notation

15.70796 \dots

Solution steps

\int_{0}^{1} π (5 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_{0}^{1} (5 x^{2})^{2} d x

Simplify

(5 x^{2})^{2} : 25 x^{4}

= π \cdot \int_{0}^{1} 25 x^{4} d x

Take the constant out:

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

= π 25 \cdot \int_{0}^{1} x^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{0}^{1}

= π 25 [\frac{x ^{5}}{5}]_{0}^{1}

Compute the boundaries:

\frac{1}{5}

= π 25 \cdot \frac{1}{5}

Simplify

= 5 π

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What is the integral from 0 to 1 of pi(5x^2)^2 ?
The integral from 0 to 1 of pi(5x^2)^2 is 5pi