What is the integral of (cos(3pi)x)/2 ?

The integral of (cos(3pi)x)/2 is -(x^2)/4+C

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integral of (cos(3pi)x)/2

\int \frac{cos ( 3 π ) x}{2} d x

- \frac{x ^{2}}{4} + C

Solution steps

\int \frac{cos ( 3 π ) x}{2} d x

Take the constant out:

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

= \frac{cos ( 3 π )}{2} \cdot \int x d x

\frac{cos ( 3 π )}{2} = - \frac{1}{2}

= (- \frac{1}{2}) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= (- \frac{1}{2}) \frac{x ^{2}}{2}

Simplify

(- \frac{1}{2}) \frac{x ^{2}}{2} : - \frac{x ^{2}}{4}

= - \frac{x ^{2}}{4}

Add a constant to the solution

= - \frac{x ^{2}}{4} + C

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What is the integral of (cos(3pi)x)/2 ?
The integral of (cos(3pi)x)/2 is -(x^2)/4+C