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

The integral from 1 to 3 of (x^2-3x) is -10/3

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

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

- \frac{10}{3}

Decimal

- 3.33333 \dots

Solution steps

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

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

\int_{1}^{3} 3 x d x = 12

= \frac{26}{3} - 12

Simplify

\frac{26}{3} - 12 : - \frac{10}{3}

= - \frac{10}{3}

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What is the integral from 1 to 3 of (x^2-3x) ?
The integral from 1 to 3 of (x^2-3x) is -10/3