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Popular >

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

Solution

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

Solution

- \frac{4}{3}

+1

Decimal Notation

- 1.33333 \dots

Solution steps

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

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

\int_{2}^{3} x^{2} d x = \frac{19}{3}

= 5 - \frac{19}{3}

Simplify

5 - \frac{19}{3} : - \frac{4}{3}

= - \frac{4}{3}

Popular Examples

integral from t to 0 of e^{ax}

\int_{t}^{0} e^{a x} d x

integral from 0 to 4 of pi|4x-x^2|

\int_{0}^{4} π 4 x - x^{2} d x

integral from-pi/4 to pi/4 of x^3sin(x)

\int_{- \frac{π}{4}}^{\frac{π}{4}} x^{3} sin (x) d x

integral from 0 to 2 of 1/(sqrt(4-s^2))

\int_{0}^{2} \frac{1}{4 - s ^{2}} d s

integral from 1 to 3 of x^2-4

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

Frequently Asked Questions (FAQ)

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