What is the integral from 1 to 7 of t^2-2t-24 ?

The integral from 1 to 7 of t^2-2t-24 is -78

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integral from 1 to 7 of t^2-2t-24

\int_{1}^{7} t^{2} - 2 t - 24 d t

- 78

Solution steps

\int_{1}^{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_{1}^{7} t^{2} d t - \int_{1}^{7} 2 t d t - \int_{1}^{7} 24 d t

\int_{1}^{7} t^{2} d t = 114

\int_{1}^{7} 2 t d t = 48

\int_{1}^{7} 24 d t = 144

= 114 - 48 - 144

Simplify

= - 78

\int_{\frac{- π}{2}}^{\frac{π}{2}} cos (x) d x

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

\int_{1}^{2} x (x - 1) d x

\int_{- 1}^{3} 2 x^{3} d x

\int_{\frac{π}{2}}^{\frac{3 π}{2}} cos (x) d x

What is the integral from 1 to 7 of t^2-2t-24 ?
The integral from 1 to 7 of t^2-2t-24 is -78