What is the integral from-2 to 6 of-t^2+6t-8 ?

The integral from-2 to 6 of-t^2+6t-8 is -128/3

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integral from-2 to 6 of-t^2+6t-8

\int_{- 2}^{6} - t^{2} + 6 t - 8 d t

- \frac{128}{3}

Decimal

- 42.66666 \dots

Solution steps

\int_{- 2}^{6} - t^{2} + 6 t - 8 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_{- 2}^{6} t^{2} d t + \int_{- 2}^{6} 6 t d t - \int_{- 2}^{6} 8 d t

\int_{- 2}^{6} t^{2} d t = \frac{224}{3}

\int_{- 2}^{6} 6 t d t = 96

\int_{- 2}^{6} 8 d t = 64

= - \frac{224}{3} + 96 - 64

Simplify

- \frac{224}{3} + 96 - 64 : - \frac{128}{3}

= - \frac{128}{3}

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What is the integral from-2 to 6 of-t^2+6t-8 ?
The integral from-2 to 6 of-t^2+6t-8 is -128/3