What is the integral from 2 to 5 of (x^2-7x+10) ?

The integral from 2 to 5 of (x^2-7x+10) is -9/2

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integral from 2 to 5 of (x^2-7x+10)

\int_{2}^{5} (x^{2} - 7 x + 10) d x

- \frac{9}{2}

Decimal

- 4.5

Solution steps

\int_{2}^{5} x^{2} - 7 x + 10 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_{2}^{5} x^{2} d x - \int_{2}^{5} 7 x d x + \int_{2}^{5} 10 d x

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} 7 x d x = \frac{147}{2}

\int_{2}^{5} 10 d x = 30

= 39 - \frac{147}{2} + 30

Simplify

39 - \frac{147}{2} + 30 : - \frac{9}{2}

= - \frac{9}{2}

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What is the integral from 2 to 5 of (x^2-7x+10) ?
The integral from 2 to 5 of (x^2-7x+10) is -9/2