What is the integral from 0 to 2 of x^2-9x+14 ?

The integral from 0 to 2 of x^2-9x+14 is 38/3

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integral from 0 to 2 of x^2-9x+14

\int_{0}^{2} x^{2} - 9 x + 14 d x

\frac{38}{3}

Decimal

12.66666 \dots

Solution steps

\int_{0}^{2} x^{2} - 9 x + 14 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} x^{2} d x - \int_{0}^{2} 9 x d x + \int_{0}^{2} 14 d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 9 x d x = 18

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

= \frac{8}{3} - 18 + 28

Simplify

\frac{8}{3} - 18 + 28 : \frac{38}{3}

= \frac{38}{3}

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What is the integral from 0 to 2 of x^2-9x+14 ?
The integral from 0 to 2 of x^2-9x+14 is 38/3