What is the integral of (1/2-1/2 cos(2θ-pi/4)) ?

The integral of (1/2-1/2 cos(2θ-pi/4)) is 1/2 θ-1/4 sin(2θ-pi/4)+C

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integral of (1/2-1/2 cos(2θ-pi/4))

\int (\frac{1}{2} - \frac{1}{2} cos (2 θ - \frac{π}{4})) d θ

\frac{1}{2} θ - \frac{1}{4} sin (2 θ - \frac{π}{4}) + C

Solution steps

\int \frac{1}{2} - \frac{1}{2} cos (2 θ - \frac{π}{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 \frac{1}{2} d θ - \int \frac{1}{2} cos (2 θ - \frac{π}{4}) d θ

\int \frac{1}{2} d θ = \frac{1}{2} θ

\int \frac{1}{2} cos (2 θ - \frac{π}{4}) d θ = \frac{1}{4} sin (2 θ - \frac{π}{4})

= \frac{1}{2} θ - \frac{1}{4} sin (2 θ - \frac{π}{4})

Add a constant to the solution

= \frac{1}{2} θ - \frac{1}{4} sin (2 θ - \frac{π}{4}) + C

1 + 0.2 t

\frac{d ^{4}}{d x ^{4}} (8 e^{- 4 x})

\frac{d y}{d x} = y (3 - y), y (0.2) = 8

\int 6 x^{2} e^{2 x} d x

\frac{d}{d x} (e^{s i n h (x)})

What is the integral of (1/2-1/2 cos(2θ-pi/4)) ?
The integral of (1/2-1/2 cos(2θ-pi/4)) is 1/2 θ-1/4 sin(2θ-pi/4)+C