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Popular >

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

Solution

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

Solution

\frac{2}{3}

+1

Decimal

0.66666 \dots

Solution steps

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

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

= 3 - \frac{7}{3}

Simplify

3 - \frac{7}{3} : \frac{2}{3}

= \frac{2}{3}

Graph

Popular Examples

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\int_{1}^{4} (5 - e) d x

integral from 0 to 3 of (x^3-4x^2+3x)

\int_{0}^{3} (x^{3} - 4 x^{2} + 3 x) d x

integral from 0 to t of e^τ

\int_{0}^{t} e^{τ} d τ

integral from 0 to 1 of 6/5 (x^2+y)

\int_{0}^{1} \frac{6}{5} (x^{2} + y) d x

integral from x^2 to x^3 of ln(t)

\int_{x^{2}}^{x^{3}} ln (t) d t

Frequently Asked Questions (FAQ)

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