What is the integral from 1 to cos(x) of 10t^9 ?

The integral from 1 to cos(x) of 10t^9 is cos^{10}(x)-1

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integral from 1 to cos(x) of 10t^9

\int_{1}^{c o s (x)} 10 t^{9} d t

cos^{10} (x) - 1

Solution steps

\int_{1}^{c o s (x)} 10 t^{9} d t

Take the constant out:

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

= 10 \cdot \int_{1}^{c o s (x)} t^{9} d t

Apply the Power Rule

: [\frac{t ^{10}}{10}]_{1}^{c o s (x)}

= 10 [\frac{t ^{10}}{10}]_{1}^{c o s (x)}

Compute the boundaries:

\frac{cos ^{10} ( x )}{10} - \frac{1}{10}

= 10 (\frac{cos ^{10} ( x )}{10} - \frac{1}{10})

Simplify

= cos^{10} (x) - 1

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What is the integral from 1 to cos(x) of 10t^9 ?
The integral from 1 to cos(x) of 10t^9 is cos^{10}(x)-1