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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

limit as x approaches 5+of 1/(x^2-25)

x \to 5 + lim (\frac{1}{x ^{2} - 25})

derivative of f(x)=arccos(-3x)derivative of

f (x) = arccos (- 3 x)

derivative of {f}(x(x^2)+({f}(x))^2)

\frac{d}{d x} (f (x) (x^{2}) + (f (x))^{2})

(\partial)/(\partial x)(1/(sqrt(x^2-y^2)))

\frac{\partial}{\partial x} (\frac{1}{x ^{2} - y ^{2}})

integral of 9y^2

\int 9 y^{2} d y

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