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

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

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integral from 0 to x of t^k

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

\frac{x ^{k + 1}}{k + 1}

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{x ^{k + 1}}{k + 1}

= \frac{x ^{k + 1}}{k + 1}

\int_{2}^{4} c x (x - 1) d x

\int_{0}^{7} 1 + x^{3} d x

\int_{0}^{3} 3 x^{2} - 24 x + 45 d x

\int_{x^{2}}^{x} \frac{sin ( x t )}{t} d t

\int_{1}^{4} \frac{x - 2}{x ( x + 1 )} d x

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