What is the integral from 0 to 8 of-t^2+3t+32 ?

The integral from 0 to 8 of-t^2+3t+32 is 544/3

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integral from 0 to 8 of-t^2+3t+32

\int_{0}^{8} - t^{2} + 3 t + 32 d t

\frac{544}{3}

Decimal

181.33333 \dots

Solution steps

\int_{0}^{8} - t^{2} + 3 t + 32 d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{0}^{8} t^{2} d t + \int_{0}^{8} 3 t d t + \int_{0}^{8} 32 d t

\int_{0}^{8} t^{2} d t = \frac{512}{3}

\int_{0}^{8} 3 t d t = 96

\int_{0}^{8} 32 d t = 256

= - \frac{512}{3} + 96 + 256

Simplify

- \frac{512}{3} + 96 + 256 : \frac{544}{3}

= \frac{544}{3}

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What is the integral from 0 to 8 of-t^2+3t+32 ?
The integral from 0 to 8 of-t^2+3t+32 is 544/3