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

The integral from 0 to 3 of (3x^2) is 27

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

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

27

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

9

= 3 \cdot 9

Simplify

= 27

\int_{- 2}^{3} x (x - 3) (x + 2) d x

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

\int_{0}^{2 π} \frac{1}{2} sin (2 θ) d θ

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

\int_{0}^{1} (x + 5) e^{x} d x

What is the integral from 0 to 3 of (3x^2) ?
The integral from 0 to 3 of (3x^2) is 27