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

The integral from 1 to 3 of x^2-2x-3 is -16/3

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

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

- \frac{16}{3}

Solution steps

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

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

\int_{1}^{3} 2 x d x = 8

\int_{1}^{3} 3 d x = 6

= \frac{26}{3} - 8 - 6

Simplify

\frac{26}{3} - 8 - 6 : - \frac{16}{3}

= - \frac{16}{3}

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What is the integral from 1 to 3 of x^2-2x-3 ?
The integral from 1 to 3 of x^2-2x-3 is -16/3