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

The integral from 3 to x^3 of t^3 is (x^{12}-81)/4

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integral from 3 to x^3 of t^3

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

\frac{x ^{12} - 81}{4}

Solution steps

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

Apply the Power Rule

: [\frac{t ^{4}}{4}]_{3}^{x^{3}}

= [\frac{t ^{4}}{4}]_{3}^{x^{3}}

Compute the boundaries:

\frac{x ^{12}}{4} - \frac{81}{4}

= \frac{x ^{12}}{4} - \frac{81}{4}

Simplify

= \frac{x ^{12} - 81}{4}

\frac{1}{x}

\frac{1}{3} x (x - 3)

2 x^{2} - 5 x + 3, at x = 0

x^{t a n (x)}

\frac{d y}{d x} = cos (y - x)

What is the integral from 3 to x^3 of t^3 ?
The integral from 3 to x^3 of t^3 is (x^{12}-81)/4