What is the integral from 7 to 9 of (x^2+2x-7) ?

The integral from 7 to 9 of (x^2+2x-7) is 440/3

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integral from 7 to 9 of (x^2+2x-7)

\int_{7}^{9} (x^{2} + 2 x - 7) d x

\frac{440}{3}

Decimal

146.66666 \dots

Solution steps

\int_{7}^{9} x^{2} + 2 x - 7 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_{7}^{9} x^{2} d x + \int_{7}^{9} 2 x d x - \int_{7}^{9} 7 d x

\int_{7}^{9} x^{2} d x = \frac{386}{3}

\int_{7}^{9} 2 x d x = 32

\int_{7}^{9} 7 d x = 14

= \frac{386}{3} + 32 - 14

Simplify

\frac{386}{3} + 32 - 14 : \frac{440}{3}

= \frac{440}{3}

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What is the integral from 7 to 9 of (x^2+2x-7) ?
The integral from 7 to 9 of (x^2+2x-7) is 440/3