What is the integral from 4 to 6 of x^2+2x-6 ?

The integral from 4 to 6 of x^2+2x-6 is 176/3

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integral from 4 to 6 of x^2+2x-6

\int_{4}^{6} x^{2} + 2 x - 6 d x

\frac{176}{3}

Decimal

58.66666 \dots

Solution steps

\int_{4}^{6} x^{2} + 2 x - 6 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_{4}^{6} x^{2} d x + \int_{4}^{6} 2 x d x - \int_{4}^{6} 6 d x

\int_{4}^{6} x^{2} d x = \frac{152}{3}

\int_{4}^{6} 2 x d x = 20

\int_{4}^{6} 6 d x = 12

= \frac{152}{3} + 20 - 12

Simplify

\frac{152}{3} + 20 - 12 : \frac{176}{3}

= \frac{176}{3}

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What is the integral from 4 to 6 of x^2+2x-6 ?
The integral from 4 to 6 of x^2+2x-6 is 176/3