What is the integral from 4 to 8 of (x^2)/2-2x+29 ?

The integral from 4 to 8 of (x^2)/2-2x+29 is 428/3

integral from 4 to 8 of (x^2)/2-2x+29

\int_{4}^{8} \frac{x ^{2}}{2} - 2 x + 29 d x

\frac{428}{3}

Decimal

142.66666 \dots

Solution steps

\int_{4}^{8} \frac{x ^{2}}{2} - 2 x + 29 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}^{8} \frac{x ^{2}}{2} d x - \int_{4}^{8} 2 x d x + \int_{4}^{8} 29 d x

\int_{4}^{8} \frac{x ^{2}}{2} d x = \frac{224}{3}

\int_{4}^{8} 2 x d x = 48

\int_{4}^{8} 29 d x = 116

= \frac{224}{3} - 48 + 116

Simplify

\frac{224}{3} - 48 + 116 : \frac{428}{3}

= \frac{428}{3}

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What is the integral from 4 to 8 of (x^2)/2-2x+29 ?
The integral from 4 to 8 of (x^2)/2-2x+29 is 428/3