What is the integral from 0 to pi/2 of sin(x)cos(y) ?

The integral from 0 to pi/2 of sin(x)cos(y) is sin(x)

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integral from 0 to pi/2 of sin(x)cos(y)

\int_{0}^{\frac{π}{2}} sin (x) cos (y) d y

sin (x)

Solution steps

\int_{0}^{\frac{π}{2}} sin (x) cos (y) d y

Take the constant out:

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

= sin (x) \cdot \int_{0}^{\frac{π}{2}} cos (y) d y

Use the common integral:

\int cos (y) d y = sin (y)

= sin (x) [sin (y)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= sin (x) \cdot 1

Simplify

= sin (x)

What is the integral from 0 to pi/2 of sin(x)cos(y) ?
The integral from 0 to pi/2 of sin(x)cos(y) is sin(x)