What is the integral from 1 to 3 of (x^2-8x+15) ?

The integral from 1 to 3 of (x^2-8x+15) is 20/3

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integral from 1 to 3 of (x^2-8x+15)

\int_{1}^{3} (x^{2} - 8 x + 15) d x

\frac{20}{3}

Solution steps

\int_{1}^{3} x^{2} - 8 x + 15 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}^{3} x^{2} d x - \int_{1}^{3} 8 x d x + \int_{1}^{3} 15 d x

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} 8 x d x = 32

\int_{1}^{3} 15 d x = 30

= \frac{26}{3} - 32 + 30

Simplify

\frac{26}{3} - 32 + 30 : \frac{20}{3}

= \frac{20}{3}

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What is the integral from 1 to 3 of (x^2-8x+15) ?
The integral from 1 to 3 of (x^2-8x+15) is 20/3