What is the integral from 3 to 6 of (-x^2+8x-10) ?

The integral from 3 to 6 of (-x^2+8x-10) is 15

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integral from 3 to 6 of (-x^2+8x-10)

\int_{3}^{6} (- x^{2} + 8 x - 10) d x

15

Solution steps

\int_{3}^{6} - x^{2} + 8 x - 10 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_{3}^{6} x^{2} d x + \int_{3}^{6} 8 x d x - \int_{3}^{6} 10 d x

\int_{3}^{6} x^{2} d x = 63

\int_{3}^{6} 8 x d x = 108

\int_{3}^{6} 10 d x = 30

= - 63 + 108 - 30

Simplify

= 15

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What is the integral from 3 to 6 of (-x^2+8x-10) ?
The integral from 3 to 6 of (-x^2+8x-10) is 15