What is the integral from x to x^2 of t^5 ?

The integral from x to x^2 of t^5 is (x^{12}-x^6)/6

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integral from x to x^2 of t^5

\int_{x}^{x^{2}} t^{5} d t

\frac{x ^{12} - x ^{6}}{6}

Solution steps

\int_{x}^{x^{2}} t^{5} d t

Apply the Power Rule

: [\frac{t ^{6}}{6}]_{x}^{x^{2}}

= [\frac{t ^{6}}{6}]_{x}^{x^{2}}

Compute the boundaries:

\frac{x ^{12}}{6} - \frac{x ^{6}}{6}

= \frac{x ^{12}}{6} - \frac{x ^{6}}{6}

Simplify

= \frac{x ^{12} - x ^{6}}{6}

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What is the integral from x to x^2 of t^5 ?
The integral from x to x^2 of t^5 is (x^{12}-x^6)/6