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

The integral from 0 to 2 of-x^2+2x+3 is 22/3

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

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

\frac{22}{3}

Solution steps

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

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

\int_{0}^{2} 3 d x = 6

= - \frac{8}{3} + 4 + 6

Simplify

- \frac{8}{3} + 4 + 6 : \frac{22}{3}

= \frac{22}{3}

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What is the integral from 0 to 2 of-x^2+2x+3 ?
The integral from 0 to 2 of-x^2+2x+3 is 22/3