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

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

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

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

\frac{22}{3}

Decimal

7.33333 \dots

Solution steps

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

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

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

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

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

Simplify

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

= \frac{22}{3}

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