What is the integral from 6 to 7 of t^2-2t-24 ?

The integral from 6 to 7 of t^2-2t-24 is 16/3

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integral from 6 to 7 of t^2-2t-24

\int_{6}^{7} t^{2} - 2 t - 24 d t

\frac{16}{3}

Decimal

5.33333 \dots

Solution steps

\int_{6}^{7} t^{2} - 2 t - 24 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_{6}^{7} t^{2} d t - \int_{6}^{7} 2 t d t - \int_{6}^{7} 24 d t

\int_{6}^{7} t^{2} d t = \frac{127}{3}

\int_{6}^{7} 2 t d t = 13

\int_{6}^{7} 24 d t = 24

= \frac{127}{3} - 13 - 24

Simplify

\frac{127}{3} - 13 - 24 : \frac{16}{3}

= \frac{16}{3}

What is the integral from 6 to 7 of t^2-2t-24 ?
The integral from 6 to 7 of t^2-2t-24 is 16/3