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Popular >

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

Solution

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

Solution

- \frac{2}{3}

+1

Decimal Notation

- 0.66666 \dots

Solution steps

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

\int_{1}^{3} 2 x d x = 8

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

= 8 - \frac{26}{3}

Simplify

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

= - \frac{2}{3}

Popular Examples

integral from 0 to 0.5 of 4x

\int_{0}^{0.5} 4 x d x

integral from 0 to pi of ((sin(x))/x)

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

integral from pi to 2pi of pi/2 sin(x)

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

integral from 1 to infinity of x/(2^x)

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

integral from 1 to 3 of sqrt(x^2+1)

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

Frequently Asked Questions (FAQ)

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