What is the integral from 0 to 2 of 15x^2+14x-8 ?

The integral from 0 to 2 of 15x^2+14x-8 is 52

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integral from 0 to 2 of 15x^2+14x-8

\int_{0}^{2} 15 x^{2} + 14 x - 8 d x

52

Solution steps

\int_{0}^{2} 15 x^{2} + 14 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_{0}^{2} 15 x^{2} d x + \int_{0}^{2} 14 x d x - \int_{0}^{2} 8 d x

\int_{0}^{2} 15 x^{2} d x = 40

\int_{0}^{2} 14 x d x = 28

\int_{0}^{2} 8 d x = 16

= 40 + 28 - 16

Simplify

= 52

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What is the integral from 0 to 2 of 15x^2+14x-8 ?
The integral from 0 to 2 of 15x^2+14x-8 is 52