What is the integral from 2 to 4 of (x^2-6x+9) ?

The integral from 2 to 4 of (x^2-6x+9) is 2/3

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integral from 2 to 4 of (x^2-6x+9)

\int_{2}^{4} (x^{2} - 6 x + 9) d x

\frac{2}{3}

Solution steps

\int_{2}^{4} x^{2} - 6 x + 9 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_{2}^{4} x^{2} d x - \int_{2}^{4} 6 x d x + \int_{2}^{4} 9 d x

\int_{2}^{4} x^{2} d x = \frac{56}{3}

\int_{2}^{4} 6 x d x = 36

\int_{2}^{4} 9 d x = 18

= \frac{56}{3} - 36 + 18

Simplify

\frac{56}{3} - 36 + 18 : \frac{2}{3}

= \frac{2}{3}

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What is the integral from 2 to 4 of (x^2-6x+9) ?
The integral from 2 to 4 of (x^2-6x+9) is 2/3