What is the integral of θcos(pi)θ ?

The integral of θcos(pi)θ is -(θ^3)/3+C

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integral of θcos(pi)θ

\int θ cos (π) θ d θ

- \frac{θ ^{3}}{3} + C

Solution steps

\int θ cos (π) θ d θ

Take the constant out:

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

= cos (π) \cdot \int θθ d θ

cos (π) = - 1

= (- 1) \cdot \int θθ d θ

Simplify

θθ : θ^{2}

= (- 1) \cdot \int θ^{2} d θ

Apply the Power Rule

: \frac{θ ^{3}}{3}

= (- 1) \frac{θ ^{3}}{3}

Simplify

= - \frac{θ ^{3}}{3}

Add a constant to the solution

= - \frac{θ ^{3}}{3} + C

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