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Popular >

integral from 0 to 1 of (1-x)^5

Solution

\int_{0}^{1} (1 - x)^{5} d x

Solution

\frac{1}{6}

+1

Solution steps

\int_{0}^{1} (1 - x)^{5} d x

Apply u-substitution

: \int_{1}^{0} - u^{5} d u

= \int_{1}^{0} - u^{5} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} - u^{5} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \int_{0}^{1} u^{5} d u)

Apply the Power Rule

: [\frac{u ^{6}}{6}]_{0}^{1}

= - (- [\frac{u ^{6}}{6}]_{0}^{1})

Simplify

= [\frac{u ^{6}}{6}]_{0}^{1}

Compute the boundaries:

\frac{1}{6}

= \frac{1}{6}

Popular Examples

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

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

integral from 0 to 2 of 10x

\int_{0}^{2} 10 x d x

integral from 6 to 7 of x

\int_{6}^{7} x d x

integral from-3 to 3 of x-|x|

\int_{- 3}^{3} x - ∣ x ∣ d x

integral from-2 to 4 of x/2+3

\int_{- 2}^{4} \frac{x}{2} + 3 d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of (1-x)^5 ?
The integral from 0 to 1 of (1-x)^5 is 1/6