What is the integral from 3 to sin(x) of x^3 ?

The integral from 3 to sin(x) of x^3 is (sin^4(x)-81)/4

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integral from 3 to sin(x) of x^3

\int_{3}^{s i n (x)} x^{3} d x

\frac{sin ^{4} ( x ) - 81}{4}

Solution steps

\int_{3}^{s i n (x)} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{3}^{s i n (x)}

= [\frac{x ^{4}}{4}]_{3}^{s i n (x)}

Compute the boundaries:

\frac{sin ^{4} ( x )}{4} - \frac{81}{4}

= \frac{sin ^{4} ( x )}{4} - \frac{81}{4}

Simplify

= \frac{sin ^{4} ( x ) - 81}{4}

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What is the integral from 3 to sin(x) of x^3 ?
The integral from 3 to sin(x) of x^3 is (sin^4(x)-81)/4