What is the integral from 5 to-5 of-1/5 x^2 ?

The integral from 5 to-5 of-1/5 x^2 is 50/3

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integral from 5 to-5 of-1/5 x^2

\int_{5}^{- 5} - \frac{1}{5} x^{2} d x

\frac{50}{3}

Decimal Notation

16.66666 \dots

Solution steps

\int_{5}^{- 5} - \frac{1}{5} x^{2} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 5}^{5} - \frac{1}{5} x^{2} d x

Take the constant out:

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

= - (- \frac{1}{5} \cdot \int_{- 5}^{5} x^{2} d x)

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{- 5}^{5}

= - (- \frac{1}{5} [\frac{x ^{3}}{3}]_{- 5}^{5})

Simplify

= \frac{1}{5} [\frac{x ^{3}}{3}]_{- 5}^{5}

Compute the boundaries:

\frac{250}{3}

= \frac{1}{5} \cdot \frac{250}{3}

Simplify

= \frac{50}{3}

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What is the integral from 5 to-5 of-1/5 x^2 ?
The integral from 5 to-5 of-1/5 x^2 is 50/3