What is the integral from 1 to 5 of t^2-2t-15 ?

The integral from 1 to 5 of t^2-2t-15 is -128/3

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integral from 1 to 5 of t^2-2t-15

\int_{1}^{5} t^{2} - 2 t - 15 d t

- \frac{128}{3}

Decimal

- 42.66666 \dots

Solution steps

\int_{1}^{5} t^{2} - 2 t - 15 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} 15 d t

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

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

\int_{1}^{5} 15 d t = 60

= \frac{124}{3} - 24 - 60

Simplify

\frac{124}{3} - 24 - 60 : - \frac{128}{3}

= - \frac{128}{3}

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\int_{4}^{7} \frac{x}{x - 3} d x

\int_{0}^{8} 11000 e^{- 0.019 t} d t

\int_{0}^{5} \frac{1}{x + 1} d x

What is the integral from 1 to 5 of t^2-2t-15 ?
The integral from 1 to 5 of t^2-2t-15 is -128/3