What is the integral from 7 to 9 of (x^2+2x-4) ?

The integral from 7 to 9 of (x^2+2x-4) is 458/3

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integral from 7 to 9 of (x^2+2x-4)

\int_{7}^{9} (x^{2} + 2 x - 4) d x

\frac{458}{3}

Decimal

152.66666 \dots

Solution steps

\int_{7}^{9} x^{2} + 2 x - 4 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} 4 d x

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

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

\int_{7}^{9} 4 d x = 8

= \frac{386}{3} + 32 - 8

Simplify

\frac{386}{3} + 32 - 8 : \frac{458}{3}

= \frac{458}{3}

What is the integral from 7 to 9 of (x^2+2x-4) ?
The integral from 7 to 9 of (x^2+2x-4) is 458/3