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

The integral from 0 to 4 of (-x^2-3x) is -136/3

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integral from 0 to 4 of (-x^2-3x)

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

- \frac{136}{3}

Decimal

- 45.33333 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 3 x d x = 24

= - \frac{64}{3} - 24

Simplify

- \frac{64}{3} - 24 : - \frac{136}{3}

= - \frac{136}{3}

What is the integral from 0 to 4 of (-x^2-3x) ?
The integral from 0 to 4 of (-x^2-3x) is -136/3