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Popular >

integral from 1 to 3 of (5x-x^2)

Solution

\int_{1}^{3} (5 x - x^{2}) d x

Solution

\frac{34}{3}

+1

Solution steps

\int_{1}^{3} 5 x - x^{2} 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_{1}^{3} 5 x d x - \int_{1}^{3} x^{2} d x

\int_{1}^{3} 5 x d x = 20

\int_{1}^{3} x^{2} d x = \frac{26}{3}

= 20 - \frac{26}{3}

Simplify

20 - \frac{26}{3} : \frac{34}{3}

= \frac{34}{3}

Popular Examples

integral from 4 to 5 of x^2

\int_{4}^{5} x^{2} d x

integral from 0 to 4 of (4-x)(sqrt(x))

\int_{0}^{4} (4 - x) (x) d x

integral from-6 to-3 of sqrt(-x-2)

\int_{- 6}^{- 3} - x - 2 d x

integral from 0 to 4 of (13-x)sqrt(x)

\int_{0}^{4} (13 - x) x d x

integral from 2 to 6 of (8x^3-6x^{-2})

\int_{2}^{6} (8 x^{3} - 6 x^{- 2}) d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to 3 of (5x-x^2) ?
The integral from 1 to 3 of (5x-x^2) is 34/3