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Popular >

integral from 0 to 1 of x-x^3

Solution

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

Solution

\frac{1}{4}

+1

Solution steps

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

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

\int_{0}^{1} 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

(\partial)/(\partial x)(e^{-x^3-y^3})

\frac{\partial}{\partial x} (e^{- x^{3} - y^{3}})

derivative of 5^t derivative of

5^{t}

f (x) = sin (x^{5})

derivative of (-5/(x^2))

\frac{d}{d x} (\frac{- 5}{x ^{2}})

integral of (2x-4)/((x^2-4x+20)^2)

\int \frac{2 x - 4}{( x ^{2} - 4 x + 20 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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