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Popular >

integral from 0 to 1 of 2x^2-x^3

Solution

\int_{0}^{1} 2 x^{2} - x^{3} d x

Solution

\frac{5}{12}

+1

Decimal Notation

0.41666 \dots

Solution steps

\int_{0}^{1} 2 x^{2} - x^{3} 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_{0}^{1} 2 x^{2} d x - \int_{0}^{1} x^{3} d x

\int_{0}^{1} 2 x^{2} d x = \frac{2}{3}

\int_{0}^{1} x^{3} d x = \frac{1}{4}

= \frac{2}{3} - \frac{1}{4}

Simplify

\frac{2}{3} - \frac{1}{4} : \frac{5}{12}

= \frac{5}{12}

Popular Examples

integral from y-1 to 1-y of x

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

integral from 0 to 4 of (2t)/(t^2-25)

\int_{0}^{4} \frac{2 t}{t ^{2} - 25} d t

integral from pi/4 to pi/2 of 2-cot^2(x)

\int_{\frac{π}{4}}^{\frac{π}{2}} 2 - cot^{2} (x) d x

integral from 0 to 1 of 4x^3sqrt(x^2+1)

\int_{0}^{1} 4 x^{3} x^{2} + 1 d x

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

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of 2x^2-x^3 ?
The integral from 0 to 1 of 2x^2-x^3 is 5/12