What is the integral from 0 to 4 of pi(2x^2)^2 ?

The integral from 0 to 4 of pi(2x^2)^2 is (4096pi)/5

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integral from 0 to 4 of pi(2x^2)^2

\int_{0}^{4} π (2 x^{2})^{2} d x

\frac{4096 π}{5}

Decimal

2573.59270 \dots

Solution steps

\int_{0}^{4} π (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_{0}^{4} (2 x^{2})^{2} d x

Simplify

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

= π \cdot \int_{0}^{4} 4 x^{4} d x

Take the constant out:

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

= π 4 \cdot \int_{0}^{4} x^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{0}^{4}

= π 4 [\frac{x ^{5}}{5}]_{0}^{4}

Compute the boundaries:

\frac{1024}{5}

= π 4 \cdot \frac{1024}{5}

Simplify

= \frac{4096 π}{5}

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\int_{1}^{2} \frac{e ^{x}}{1 + 2 e ^{x}} d x

What is the integral from 0 to 4 of pi(2x^2)^2 ?
The integral from 0 to 4 of pi(2x^2)^2 is (4096pi)/5