What is the integral of-cos(x-y) ?

The integral of-cos(x-y) is sin(x-y)+C

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integral of-cos(x-y)

\int - cos (x - y) d y

sin (x - y) + C

Solution steps

\int - cos (x - y) d y

Take the constant out:

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

= - \int cos (x - y) d y

Apply u-substitution

: \int - cos (u) d u

= - \int - cos (u) d u

Take the constant out:

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

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

Use the common integral:

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

= - (- sin (u))

Substitute back

u = x - y

= - (- sin (x - y))

Simplify

= sin (x - y)

Add a constant to the solution

= sin (x - y) + C

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