What is the integral from 0 to 2 of (4x^2) ?

The integral from 0 to 2 of (4x^2) is 32/3

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integral from 0 to 2 of (4x^2)

\int_{0}^{2} (4 x^{2}) d x

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

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

Take the constant out:

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

= 4 \cdot \int_{0}^{2} x^{2} d x

Apply the Power Rule

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

= 4 [\frac{x ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= 4 \cdot \frac{8}{3}

Simplify

= \frac{32}{3}

\int_{2}^{\infty} \frac{2}{x ^{2}} d x

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\int_{1}^{2} (15 x^{4} - 4 x) d x

What is the integral from 0 to 2 of (4x^2) ?
The integral from 0 to 2 of (4x^2) is 32/3