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

The integral from 0 to 2 of (3x)^2 is 24

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

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

24

Solution steps

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

Simplify

(3 x)^{2} : 9 x^{2}

= \int_{0}^{2} 9 x^{2} d x

Take the constant out:

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

= 9 \cdot \int_{0}^{2} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{2}

= 9 [\frac{x ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= 9 \cdot \frac{8}{3}

Simplify

= 24

\int_{0}^{\frac{1}{2}} (1 - x^{2})^{\frac{1}{2}} d x

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\int_{0}^{1} (1 - x^{2})^{\frac{5}{2}} d x

\int_{- 2 π}^{3 π} cos^{2} (x) d x

What is the integral from 0 to 2 of (3x)^2 ?
The integral from 0 to 2 of (3x)^2 is 24