What is the integral from 3 to 5 of-x^2+7x-10 ?

The integral from 3 to 5 of-x^2+7x-10 is 10/3

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integral from 3 to 5 of-x^2+7x-10

\int_{3}^{5} - x^{2} + 7 x - 10 d x

\frac{10}{3}

Decimal Notation

3.33333 \dots

Solution steps

\int_{3}^{5} - 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_{3}^{5} x^{2} d x + \int_{3}^{5} 7 x d x - \int_{3}^{5} 10 d x

\int_{3}^{5} x^{2} d x = \frac{98}{3}

\int_{3}^{5} 7 x d x = 56

\int_{3}^{5} 10 d x = 20

= - \frac{98}{3} + 56 - 20

Simplify

- \frac{98}{3} + 56 - 20 : \frac{10}{3}

= \frac{10}{3}

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What is the integral from 3 to 5 of-x^2+7x-10 ?
The integral from 3 to 5 of-x^2+7x-10 is 10/3