What is the integral of (sin(θ)-cos(θ)) ?

The integral of (sin(θ)-cos(θ)) is -cos(θ)-sin(θ)+C

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integral of (sin(θ)-cos(θ))

\int (sin (θ) - cos (θ)) d θ

- cos (θ) - sin (θ) + C

Solution steps

\int sin (θ) - cos (θ) d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (θ) d θ - \int cos (θ) d θ

\int sin (θ) d θ = - cos (θ)

\int cos (θ) d θ = sin (θ)

= - cos (θ) - sin (θ)

Add a constant to the solution

= - cos (θ) - sin (θ) + C

What is the integral of (sin(θ)-cos(θ)) ?
The integral of (sin(θ)-cos(θ)) is -cos(θ)-sin(θ)+C