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Popular >

integral from 1 to 3 of-x^2+4

Solution

\int_{1}^{3} - x^{2} + 4 d x

Solution

- \frac{2}{3}

+1

Solution steps

\int_{1}^{3} - x^{2} + 4 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} x^{2} d x + \int_{1}^{3} 4 d x

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

\int_{1}^{3} 4 d x = 8

= - \frac{26}{3} + 8

Simplify

- \frac{26}{3} + 8 : - \frac{2}{3}

= - \frac{2}{3}

Popular Examples

integral from 2 to 1 of 1/x

\int_{2}^{1} \frac{1}{x} d x

integral from 0 to pi/3 of 5sin(x/2)

\int_{0}^{\frac{π}{3}} 5 sin (\frac{x}{2}) d x

integral from 0 to 120 of 5-5e^{-0.2x}

\int_{0}^{120} 5 - 5 e^{- 0.2 x} d x

integral from 1/4 to 1/2 of x/2

\int_{\frac{1}{4}}^{\frac{1}{2}} \frac{x}{2} d x

integral from 0 to x of 2

\int_{0}^{x} 2 d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to 3 of-x^2+4 ?
The integral from 1 to 3 of-x^2+4 is -2/3