What is the integral from 1 to 4 of-2x^2+10x-8 ?

The integral from 1 to 4 of-2x^2+10x-8 is 9

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integral from 1 to 4 of-2x^2+10x-8

\int_{1}^{4} - 2 x^{2} + 10 x - 8 d x

9

Solution steps

\int_{1}^{4} - 2 x^{2} + 10 x - 8 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_{1}^{4} 2 x^{2} d x + \int_{1}^{4} 10 x d x - \int_{1}^{4} 8 d x

\int_{1}^{4} 2 x^{2} d x = 42

\int_{1}^{4} 10 x d x = 75

\int_{1}^{4} 8 d x = 24

= - 42 + 75 - 24

Simplify

= 9

What is the integral from 1 to 4 of-2x^2+10x-8 ?
The integral from 1 to 4 of-2x^2+10x-8 is 9