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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

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 5 to 9 of (x-5)

\int_{5}^{9} (x - 5) d x

integral from 0 to t of (t-w)e^{7w}

\int_{0}^{t} (t - w) e^{7 w} d w

integral from 1 to 4 of (x+3)

\int_{1}^{4} (x + 3) d x

integral from-1 to 5 of (3-|x|)

\int_{- 1}^{5} (3 - ∣ x ∣) d x

integral from 0 to 1 of sqrt(8x+1)

\int_{0}^{1} 8 x + 1 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