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Popular >

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

Solution

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

Solution

- \frac{1}{4}

+1

Decimal Notation

- 0.25

Solution steps

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

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

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

= - \frac{1}{2} - (- \frac{1}{4})

Simplify

- \frac{1}{2} - (- \frac{1}{4}) : - \frac{1}{4}

= - \frac{1}{4}

Popular Examples

integral from 2 to 3 of (3x^2-2x+7)

\int_{2}^{3} (3 x^{2} - 2 x + 7) d x

integral from 0 to 1 of (2-2y^2)^3

\int_{0}^{1} (2 - 2 y^{2})^{3} d y

integral from 1 to 4 of sqrt(x)-x+2

\int_{1}^{4} x - x + 2 d x

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

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

integral from 0 to 3 of 1/((x+5)(x^2+9))

\int_{0}^{3} \frac{1}{( x + 5 ) ( x ^{2} + 9 )} d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 0 of (x-x^3) ?
The integral from-1 to 0 of (x-x^3) is -1/4