What is the integral from-4 to 6 of 12+x-1/2 x^2 ?

The integral from-4 to 6 of 12+x-1/2 x^2 is 250/3

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integral from-4 to 6 of 12+x-1/2 x^2

\int_{- 4}^{6} 12 + x - \frac{1}{2} x^{2} d x

\frac{250}{3}

Decimal

83.33333 \dots

Solution steps

\int_{- 4}^{6} 12 + x - \frac{1}{2} x^{2} 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_{- 4}^{6} 12 d x + \int_{- 4}^{6} x d x - \int_{- 4}^{6} \frac{1}{2} x^{2} d x

\int_{- 4}^{6} 12 d x = 120

\int_{- 4}^{6} x d x = 10

\int_{- 4}^{6} \frac{1}{2} x^{2} d x = \frac{140}{3}

= 120 + 10 - \frac{140}{3}

Simplify

120 + 10 - \frac{140}{3} : \frac{250}{3}

= \frac{250}{3}

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What is the integral from-4 to 6 of 12+x-1/2 x^2 ?
The integral from-4 to 6 of 12+x-1/2 x^2 is 250/3