What is the integral of-cos(θ)+sin(θ)+4 ?

The integral of-cos(θ)+sin(θ)+4 is -sin(θ)-cos(θ)+4θ+C

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integral of-cos(θ)+sin(θ)+4

\int - cos (θ) + sin (θ) + 4 d θ

- sin (θ) - cos (θ) + 4 θ + C

Solution steps

\int - cos (θ) + sin (θ) + 4 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 cos (θ) d θ + \int sin (θ) d θ + \int 4 d θ

\int cos (θ) d θ = sin (θ)

\int sin (θ) d θ = - cos (θ)

\int 4 d θ = 4 θ

= - sin (θ) - cos (θ) + 4 θ

Add a constant to the solution

= - sin (θ) - cos (θ) + 4 θ + C

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What is the integral of-cos(θ)+sin(θ)+4 ?
The integral of-cos(θ)+sin(θ)+4 is -sin(θ)-cos(θ)+4θ+C