What is the integral from 0 to 4 of (x^2)/8 ?

The integral from 0 to 4 of (x^2)/8 is 8/3

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integral from 0 to 4 of (x^2)/8

\int_{0}^{4} \frac{x ^{2}}{8} d x

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

\int_{0}^{4} \frac{x ^{2}}{8} d x

Take the constant out:

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

= \frac{1}{8} \cdot \int_{0}^{4} x^{2} d x

Apply the Power Rule

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

= \frac{1}{8} [\frac{x ^{3}}{3}]_{0}^{4}

Compute the boundaries:

\frac{64}{3}

= \frac{1}{8} \cdot \frac{64}{3}

Simplify

= \frac{8}{3}

\int_{0}^{\frac{π}{2}} 4 cos (x) d x

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

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

\int_{- 2}^{2} (x^{2} - y^{2}) d y

What is the integral from 0 to 4 of (x^2)/8 ?
The integral from 0 to 4 of (x^2)/8 is 8/3