What is the integral from 0 to 2 of 8x^2 ?

The integral from 0 to 2 of 8x^2 is 64/3

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integral from 0 to 2 of 8x^2

\int_{0}^{2} 8 x^{2} d x

\frac{64}{3}

Decimal

21.33333 \dots

Solution steps

\int_{0}^{2} 8 x^{2} d x

Take the constant out:

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

= 8 \cdot \int_{0}^{2} x^{2} d x

Apply the Power Rule

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

= 8 [\frac{x ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

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

Simplify

= \frac{64}{3}

\int_{a}^{\infty} x^{n} d x

\int_{24}^{25} x x^{2} - 576 d x

\int_{- 1}^{3} 3 x^{2} - 6 x d x

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\int_{1}^{0} \frac{1}{x} d x

What is the integral from 0 to 2 of 8x^2 ?
The integral from 0 to 2 of 8x^2 is 64/3