What is the integral from 5 to 6 of x^2+2x+2-18 ?

The integral from 5 to 6 of x^2+2x+2-18 is 76/3

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integral from 5 to 6 of x^2+2x+2-18

\int_{5}^{6} x^{2} + 2 x + 2 - 18 d x

\frac{76}{3}

Decimal

25.33333 \dots

Solution steps

\int_{5}^{6} x^{2} + 2 x + 2 - 18 d x

Simplify

= \int_{5}^{6} x^{2} + 2 x - 16 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_{5}^{6} x^{2} d x + \int_{5}^{6} 2 x d x - \int_{5}^{6} 16 d x

\int_{5}^{6} x^{2} d x = \frac{91}{3}

\int_{5}^{6} 2 x d x = 11

\int_{5}^{6} 16 d x = 16

= \frac{91}{3} + 11 - 16

Simplify

\frac{91}{3} + 11 - 16 : \frac{76}{3}

= \frac{76}{3}

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What is the integral from 5 to 6 of x^2+2x+2-18 ?
The integral from 5 to 6 of x^2+2x+2-18 is 76/3