What is the integral from 5 to 7 of x^2+2x+2-18 ?

The integral from 5 to 7 of x^2+2x+2-18 is 194/3

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integral from 5 to 7 of x^2+2x+2-18

\int_{5}^{7} x^{2} + 2 x + 2 - 18 d x

\frac{194}{3}

Decimal Notation

64.66666 \dots

Solution steps

\int_{5}^{7} x^{2} + 2 x + 2 - 18 d x

Simplify

= \int_{5}^{7} 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}^{7} x^{2} d x + \int_{5}^{7} 2 x d x - \int_{5}^{7} 16 d x

\int_{5}^{7} x^{2} d x = \frac{218}{3}

\int_{5}^{7} 2 x d x = 24

\int_{5}^{7} 16 d x = 32

= \frac{218}{3} + 24 - 32

Simplify

\frac{218}{3} + 24 - 32 : \frac{194}{3}

= \frac{194}{3}

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What is the integral from 5 to 7 of x^2+2x+2-18 ?
The integral from 5 to 7 of x^2+2x+2-18 is 194/3