What is the integral from a to x of t^4 ?

The integral from a to x of t^4 is (x^5-a^5)/5

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integral from a to x of t^4

\int_{a}^{x} t^{4} d t

\frac{x ^{5} - a ^{5}}{5}

Solution steps

\int_{a}^{x} t^{4} d t

Apply the Power Rule

= [\frac{t ^{5}}{5}]_{a}^{x}

Compute the boundaries:

\frac{x ^{5}}{5} - \frac{a ^{5}}{5}

= \frac{x ^{5}}{5} - \frac{a ^{5}}{5}

Simplify

= \frac{x ^{5} - a ^{5}}{5}

What is the integral from a to x of t^4 ?
The integral from a to x of t^4 is (x^5-a^5)/5