What is the integral from 3 to 5 of t^2+2t-15 ?

The integral from 3 to 5 of t^2+2t-15 is 56/3

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integral from 3 to 5 of t^2+2t-15

\int_{3}^{5} t^{2} + 2 t - 15 d t

\frac{56}{3}

Solution steps

\int_{3}^{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_{3}^{5} t^{2} d t + \int_{3}^{5} 2 t d t - \int_{3}^{5} 15 d t

\int_{3}^{5} t^{2} d t = \frac{98}{3}

\int_{3}^{5} 2 t d t = 16

\int_{3}^{5} 15 d t = 30

= \frac{98}{3} + 16 - 30

Simplify

\frac{98}{3} + 16 - 30 : \frac{56}{3}

= \frac{56}{3}

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What is the integral from 3 to 5 of t^2+2t-15 ?
The integral from 3 to 5 of t^2+2t-15 is 56/3