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

The integral from 0 to 2 of pi(2x)^2 is (32pi)/3

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

\int_{0}^{2} π (2 x)^{2} d x

\frac{32 π}{3}

Decimal

33.51032 \dots

Solution steps

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

Simplify

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

= π \cdot \int_{0}^{2} 4 x^{2} 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}^{2} x^{2} d x

Apply the Power Rule

= π 4 [\frac{x ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= π 4 \cdot \frac{8}{3}

Simplify

= \frac{32 π}{3}

What is the integral from 0 to 2 of pi(2x)^2 ?
The integral from 0 to 2 of pi(2x)^2 is (32pi)/3