What is the integral from 0 to 1 of pi(7x^2)^2 ?

The integral from 0 to 1 of pi(7x^2)^2 is (49pi)/5

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integral from 0 to 1 of pi(7x^2)^2

\int_{0}^{1} π (7 x^{2})^{2} d x

\frac{49 π}{5}

Decimal

30.78760 \dots

Solution steps

\int_{0}^{1} π (7 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} (7 x^{2})^{2} d x

Simplify

(7 x^{2})^{2} : 49 x^{4}

= π \cdot \int_{0}^{1} 49 x^{4} d x

Take the constant out:

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

= π 49 \cdot \int_{0}^{1} x^{4} d x

Apply the Power Rule

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

= π 49 [\frac{x ^{5}}{5}]_{0}^{1}

Compute the boundaries:

\frac{1}{5}

= π 49 \cdot \frac{1}{5}

Simplify

= \frac{49 π}{5}

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What is the integral from 0 to 1 of pi(7x^2)^2 ?
The integral from 0 to 1 of pi(7x^2)^2 is (49pi)/5