What is the integral from 0 to sin(x) of e^ycos(x) ?

The integral from 0 to sin(x) of e^ycos(x) is cos(x)(e^{sin(x)}-1)

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integral from 0 to sin(x) of e^ycos(x)

\int_{0}^{s i n (x)} e^{y} cos (x) d y

cos (x) (e^{s i n (x)} - 1)

Solution steps

\int_{0}^{s i n (x)} e^{y} cos (x) d y

Take the constant out:

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

= cos (x) \cdot \int_{0}^{s i n (x)} e^{y} d y

Use the common integral:

\int e^{y} d y = e^{y}

= cos (x) [e^{y}]_{0}^{s i n (x)}

Compute the boundaries:

e^{s i n (x)} - 1

= cos (x) (e^{s i n (x)} - 1)

What is the integral from 0 to sin(x) of e^ycos(x) ?
The integral from 0 to sin(x) of e^ycos(x) is cos(x)(e^{sin(x)}-1)