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

The integral from-1 to 3 of (1/2 x^2-2x-3) is -46/3

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

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

- \frac{46}{3}

Decimal

- 15.33333 \dots

Solution steps

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

\int_{- 1}^{3} \frac{1}{2} x^{2} d x = \frac{14}{3}

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

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

= \frac{14}{3} - 8 - 12

Simplify

\frac{14}{3} - 8 - 12 : - \frac{46}{3}

= - \frac{46}{3}

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What is the integral from-1 to 3 of (1/2 x^2-2x-3) ?
The integral from-1 to 3 of (1/2 x^2-2x-3) is -46/3