What is the integral from 1 to 5 of (2+3x-x^2) ?

The integral from 1 to 5 of (2+3x-x^2) is 8/3

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integral from 1 to 5 of (2+3x-x^2)

\int_{1}^{5} (2 + 3 x - x^{2}) d x

\frac{8}{3}

Solution steps

\int_{1}^{5} 2 + 3 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_{1}^{5} 2 d x + \int_{1}^{5} 3 x d x - \int_{1}^{5} x^{2} d x

\int_{1}^{5} 2 d x = 8

\int_{1}^{5} 3 x d x = 36

\int_{1}^{5} x^{2} d x = \frac{124}{3}

= 8 + 36 - \frac{124}{3}

Simplify

8 + 36 - \frac{124}{3} : \frac{8}{3}

= \frac{8}{3}

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What is the integral from 1 to 5 of (2+3x-x^2) ?
The integral from 1 to 5 of (2+3x-x^2) is 8/3