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

The integral from 0 to 2 of (3x^2) is 8

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

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

8

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{8}{3}

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

Simplify

= 8

\int_{1}^{2} x^{3} - 3 x^{2} + 2 x d x

\int_{0}^{1} x^{2} 1 + 4 x^{2} d x

\int_{0}^{5} 5 ln (x) d x

\int_{3}^{4} - lo g_{9} (t) d t

\int_{- 3}^{3} \frac{1}{x ^{2}} d x

What is the integral from 0 to 2 of (3x^2) ?
The integral from 0 to 2 of (3x^2) is 8