What is the integral from 1 to sin(x) of 12t^{11} ?

The integral from 1 to sin(x) of 12t^{11} is sin^{12}(x)-1

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integral from 1 to sin(x) of 12t^{11}

\int_{1}^{s i n (x)} 12 t^{11} d t

sin^{12} (x) - 1

Solution steps

\int_{1}^{s i n (x)} 12 t^{11} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 12 \cdot \int_{1}^{s i n (x)} t^{11} d t

Apply the Power Rule

: [\frac{t ^{12}}{12}]_{1}^{s i n (x)}

= 12 [\frac{t ^{12}}{12}]_{1}^{s i n (x)}

Compute the boundaries:

\frac{sin ^{12} ( x )}{12} - \frac{1}{12}

= 12 (\frac{sin ^{12} ( x )}{12} - \frac{1}{12})

Simplify

= sin^{12} (x) - 1

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What is the integral from 1 to sin(x) of 12t^{11} ?
The integral from 1 to sin(x) of 12t^{11} is sin^{12}(x)-1