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(x+pi/2)-sin(x)

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

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

sin (x + \frac{π}{2}) - sin (x)

Solution steps

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

Apply u-substitution

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

Use the common integral:

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

= [sin (u)]_{x}^{x + \frac{π}{2}}

Compute the boundaries:

sin (x + \frac{π}{2}) - sin (x)

= sin (x + \frac{π}{2}) - sin (x)

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(x+pi/2)-sin(x)