What is the integral from 2 to 5 of (x^2-2x-4) ?

The integral from 2 to 5 of (x^2-2x-4) is 6

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integral from 2 to 5 of (x^2-2x-4)

\int_{2}^{5} (x^{2} - 2 x - 4) d x

6

Solution steps

\int_{2}^{5} x^{2} - 2 x - 4 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{2}^{5} x^{2} d x - \int_{2}^{5} 2 x d x - \int_{2}^{5} 4 d x

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} 2 x d x = 21

\int_{2}^{5} 4 d x = 12

= 39 - 21 - 12

Simplify

= 6

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

\int_{1}^{3} 5 x (x^{2} + 4) d x

\int_{1}^{x^{2}} ln (t) d t

\int_{- 1}^{1} 3 x^{2} e^{3 x^{3} - 7} d x

\int_{0}^{2} 11 x (x^{2} + 1)^{2} d x

What is the integral from 2 to 5 of (x^2-2x-4) ?
The integral from 2 to 5 of (x^2-2x-4) is 6