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Popular >

integral from 0 to 1 of x^2(1-x)

Solution

\int_{0}^{1} x^{2} (1 - x) d x

Solution

\frac{1}{12}

+1

Decimal Notation

0.08333 \dots

Solution steps

\int_{0}^{1} x^{2} (1 - x) d x

Expand

x^{2} (1 - x) : x^{2} - x^{3}

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

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

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

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

Simplify

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

= \frac{1}{12}

Popular Examples

integral from 0 to 1 of e^{-st}t^2

\int_{0}^{1} e^{- s t} t^{2} d t

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

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

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

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

integral from 0 to y of y

\int_{0}^{y} y d y

integral from 0 to 1 of 1/((3x-2)^4)

\int_{0}^{1} \frac{1}{( 3 x - 2 ) ^{4}} d x

Frequently Asked Questions (FAQ)

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