What is the integral of 10picos(2pi)x ?

The integral of 10picos(2pi)x is 5pix^2+C

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integral of 10picos(2pi)x

\int 10 π cos (2 π) x d x

5 π x^{2} + C

Solution steps

\int 10 π cos (2 π) x d x

Take the constant out:

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

= 10 π cos (2 π) \cdot \int x d x

10 π cos (2 π) = 10 π

= 10 π \cdot \int x d x

Apply the Power Rule

= 10 π \frac{x ^{2}}{2}

Simplify

10 π \frac{x ^{2}}{2} : 5 π x^{2}

= 5 π x^{2}

Add a constant to the solution

= 5 π x^{2} + C

What is the integral of 10picos(2pi)x ?
The integral of 10picos(2pi)x is 5pix^2+C