What is the integral from 1 to 2 of (-3x^2+6x+5) ?

The integral from 1 to 2 of (-3x^2+6x+5) is 7

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integral from 1 to 2 of (-3x^2+6x+5)

\int_{1}^{2} (- 3 x^{2} + 6 x + 5) d x

7

Solution steps

\int_{1}^{2} - 3 x^{2} + 6 x + 5 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}^{2} 3 x^{2} d x + \int_{1}^{2} 6 x d x + \int_{1}^{2} 5 d x

\int_{1}^{2} 3 x^{2} d x = 7

\int_{1}^{2} 6 x d x = 9

\int_{1}^{2} 5 d x = 5

= - 7 + 9 + 5

Simplify

= 7

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What is the integral from 1 to 2 of (-3x^2+6x+5) ?
The integral from 1 to 2 of (-3x^2+6x+5) is 7