What is the integral of (3-y)cos(x) ?

The integral of (3-y)cos(x) is cos(x)(3y-(y^2)/2)+C

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integral of (3-y)cos(x)

\int (3 - y) cos (x)

cos (x) (3 y - \frac{y ^{2}}{2}) + C

Solution steps

\int (3 - y) cos (x) d y

Take the constant out:

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

= cos (x) \cdot \int 3 - y d y

Apply the Sum Rule:

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

= cos (x) (\int 3 d y - \int y d y)

\int 3 d y = 3 y

\int y d y = \frac{y ^{2}}{2}

= cos (x) (3 y - \frac{y ^{2}}{2})

Add a constant to the solution

= cos (x) (3 y - \frac{y ^{2}}{2}) + C

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What is the integral of (3-y)cos(x) ?
The integral of (3-y)cos(x) is cos(x)(3y-(y^2)/2)+C