What is the integral from 0 to 3 of-x^2+x^2-4x ?

The integral from 0 to 3 of-x^2+x^2-4x is -18

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integral from 0 to 3 of-x^2+x^2-4x

\int_{0}^{3} - x^{2} + x^{2} - 4 x d x

- 18

Solution steps

\int_{0}^{3} - x^{2} + x^{2} - 4 x d x

Simplify

= \int_{0}^{3} - 4 x d x

Take the constant out:

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

= - 4 \cdot \int_{0}^{3} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{9}{2}

= - 4 \cdot \frac{9}{2}

Simplify

= - 18

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What is the integral from 0 to 3 of-x^2+x^2-4x ?
The integral from 0 to 3 of-x^2+x^2-4x is -18