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

The integral from 0 to 3 of pi(2x)^2 is 36pi

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integral from 0 to 3 of pi(2x)^2

\int_{0}^{3} π (2 x)^{2} d x

36 π

Decimal Notation

113.09733 \dots

Solution steps

\int_{0}^{3} 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}^{3} (2 x)^{2} d x

Simplify

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

= π \cdot \int_{0}^{3} 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}^{3} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{3}

= π 4 [\frac{x ^{3}}{3}]_{0}^{3}

Compute the boundaries:

9

= π 4 \cdot 9

Simplify

= 36 π

\int \frac{1}{( 1 - y ^{2} ) ^{\frac{1}{2}}} d y

\int \frac{x + 1}{x ^{2} + 2 x + 2} d x

\int \frac{x ^{2} - 4}{x ^{3} - 2 x ^{2} + x} d x

\frac{d}{d x} (2^{x s i n (x)})

f (x) = 5 tan (x)

What is the integral from 0 to 3 of pi(2x)^2 ?
The integral from 0 to 3 of pi(2x)^2 is 36pi