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

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

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

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

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

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

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

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

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

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

Simplify

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

= \frac{8}{3}

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