What is the integral of 2picos(pi)x ?

The integral of 2picos(pi)x is -pix^2+C

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integral of 2picos(pi)x

\int 2 π cos (π) x d x

- π x^{2} + C

Solution steps

\int 2 π cos (π) x d x

Take the constant out:

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

= 2 π cos (π) \cdot \int x d x

2 π cos (π) = - 2 π

= (- 2 π) \cdot \int x d x

Apply the Power Rule

= (- 2 π) \frac{x ^{2}}{2}

Simplify

(- 2 π) \frac{x ^{2}}{2} : - π x^{2}

= - π x^{2}

Add a constant to the solution

= - π x^{2} + C