What is the integral from 1 to 5 of t^2-2t-8 ?

The integral from 1 to 5 of t^2-2t-8 is -44/3

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integral from 1 to 5 of t^2-2t-8

\int_{1}^{5} t^{2} - 2 t - 8 d t

- \frac{44}{3}

Solution steps

\int_{1}^{5} t^{2} - 2 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_{1}^{5} t^{2} d t - \int_{1}^{5} 2 t d t - \int_{1}^{5} 8 d t

\int_{1}^{5} t^{2} d t = \frac{124}{3}

\int_{1}^{5} 2 t d t = 24

\int_{1}^{5} 8 d t = 32

= \frac{124}{3} - 24 - 32

Simplify

\frac{124}{3} - 24 - 32 : - \frac{44}{3}

= - \frac{44}{3}

\int_{- 3}^{2} 12 - x^{2} - x d x

\int_{2}^{3} x^{2} - x - 2 d x

\int_{0}^{2} 3 x + 1 d x

\int_{- 3}^{- 1} \frac{t + 1}{t ^{3}} d t

\int_{0}^{4} 6 x^{3} d x

What is the integral from 1 to 5 of t^2-2t-8 ?
The integral from 1 to 5 of t^2-2t-8 is -44/3