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

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

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

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

sin (- y + \frac{π}{2}) + sin (y)

Solution steps

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

Apply u-substitution

= \int_{- y}^{- y + \frac{π}{2}} cos (u) d u

Use the common integral:

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

= [sin (u)]_{- y}^{- y + \frac{π}{2}}

Compute the boundaries:

sin (- y + \frac{π}{2}) + sin (y)

= sin (- y + \frac{π}{2}) + sin (y)

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