What is the integral from x to x^2 of t^3 ?

The integral from x to x^2 of t^3 is (x^8-x^4)/4

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integral from x to x^2 of t^3

\int_{x}^{x^{2}} t^{3} d t

\frac{x ^{8} - x ^{4}}{4}

Solution steps

\int_{x}^{x^{2}} t^{3} d t

Apply the Power Rule

: [\frac{t ^{4}}{4}]_{x}^{x^{2}}

= [\frac{t ^{4}}{4}]_{x}^{x^{2}}

Compute the boundaries:

\frac{x ^{8}}{4} - \frac{x ^{4}}{4}

= \frac{x ^{8}}{4} - \frac{x ^{4}}{4}

Simplify

= \frac{x ^{8} - x ^{4}}{4}

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What is the integral from x to x^2 of t^3 ?
The integral from x to x^2 of t^3 is (x^8-x^4)/4