What is the integral from 2 to 4 of x^2-7x+10 ?

The integral from 2 to 4 of x^2-7x+10 is -10/3

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integral from 2 to 4 of x^2-7x+10

\int_{2}^{4} x^{2} - 7 x + 10 d x

- \frac{10}{3}

Solution steps

\int_{2}^{4} x^{2} - 7 x + 10 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} 7 x d x + \int_{2}^{4} 10 d x

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

\int_{2}^{4} 7 x d x = 42

\int_{2}^{4} 10 d x = 20

= \frac{56}{3} - 42 + 20

Simplify

\frac{56}{3} - 42 + 20 : - \frac{10}{3}

= - \frac{10}{3}

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What is the integral from 2 to 4 of x^2-7x+10 ?
The integral from 2 to 4 of x^2-7x+10 is -10/3