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Popular >

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

Solution

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

Solution

- \frac{1}{12}

+1

Decimal Notation

- 0.08333 \dots

Solution steps

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

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

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

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

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

Simplify

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

= - \frac{1}{12}

Popular Examples

integral from-1 to 3 of x^{-3}

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

integral from 0 to 3 of e^{-1/2 x}

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

integral from 0 to-infinity of e^{3x}

\int_{0}^{- \infty} e^{3 x} d x

integral from 0 to pi/4 of (cos(x))

\int_{0}^{\frac{π}{4}} (cos (x)) d x

integral from 1 to 3 of sqrt(9-x^2)

\int_{1}^{3} 9 - x^{2} d x

Frequently Asked Questions (FAQ)

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