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Popular >

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

Solution

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

Solution

- \frac{9}{4}

+1

Decimal

- 2.25

Solution steps

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

Expand

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

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

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

\int_{- 1}^{2} x^{3} d x = \frac{15}{4}

= \frac{3}{2} - \frac{15}{4}

Simplify

\frac{3}{2} - \frac{15}{4} : - \frac{9}{4}

= - \frac{9}{4}

Graph

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\int_{0}^{\frac{π}{3}} sin (3 y) cos (y) d y

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\int_{0}^{0} 16 - t^{2} d t

integral from-1 to 3 of (-x+2)

\int_{- 1}^{3} (- x + 2) d x

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\int_{1}^{5} 3 + 4 x^{- 4} d x

integral from 1 to infinity of 1/y

\int_{1}^{\infty} \frac{1}{y} d y

Frequently Asked Questions (FAQ)

What is the integral from-1 to 2 of x(1-x^2) ?
The integral from-1 to 2 of x(1-x^2) is -9/4