What is the integral from 0 to 1 of x^k ?

The integral from 0 to 1 of x^k is 1/(k+1)

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integral from 0 to 1 of x^k

\int_{0}^{1} x^{k} d x

\frac{1}{k + 1}

Solution steps

\int_{0}^{1} x^{k} d x

Apply the Power Rule

: [\frac{x ^{k + 1}}{k + 1}]_{0}^{1}

= [\frac{x ^{k + 1}}{k + 1}]_{0}^{1}

Compute the boundaries:

\frac{1}{k + 1}

= \frac{1}{k + 1}

\int \frac{x ^{3}}{( x + 3 ) ^{4}} d x

x \to 0 lim (- \frac{1}{x ^{4}})

\int A^{2} d A

\frac{d y}{d t} + 2 y = 3 e^{- t}, y (0) = 1

\int 5 cos (x) d x

What is the integral from 0 to 1 of x^k ?
The integral from 0 to 1 of x^k is 1/(k+1)