What is the integral from 1 to cos(x) of 6t^5 ?

The integral from 1 to cos(x) of 6t^5 is cos^6(x)-1

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integral from 1 to cos(x) of 6t^5

\int_{1}^{c o s (x)} 6 t^{5} d t

cos^{6} (x) - 1

Solution steps

\int_{1}^{c o s (x)} 6 t^{5} d t

Take the constant out:

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

= 6 \cdot \int_{1}^{c o s (x)} t^{5} d t

Apply the Power Rule

= 6 [\frac{t ^{6}}{6}]_{1}^{c o s (x)}

Compute the boundaries:

\frac{cos ^{6} ( x )}{6} - \frac{1}{6}

= 6 (\frac{cos ^{6} ( x )}{6} - \frac{1}{6})

Simplify

= cos^{6} (x) - 1

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What is the integral from 1 to cos(x) of 6t^5 ?
The integral from 1 to cos(x) of 6t^5 is cos^6(x)-1