What is the integral from 0 to 5 of x^2+2x-15 ?

The integral from 0 to 5 of x^2+2x-15 is -25/3

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integral from 0 to 5 of x^2+2x-15

\int_{0}^{5} x^{2} + 2 x - 15 d x

- \frac{25}{3}

Decimal

- 8.33333 \dots

Solution steps

\int_{0}^{5} x^{2} + 2 x - 15 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}^{5} x^{2} d x + \int_{0}^{5} 2 x d x - \int_{0}^{5} 15 d x

\int_{0}^{5} x^{2} d x = \frac{125}{3}

\int_{0}^{5} 2 x d x = 25

\int_{0}^{5} 15 d x = 75

= \frac{125}{3} + 25 - 75

Simplify

\frac{125}{3} + 25 - 75 : - \frac{25}{3}

= - \frac{25}{3}

What is the integral from 0 to 5 of x^2+2x-15 ?
The integral from 0 to 5 of x^2+2x-15 is -25/3