What is the integral of tcos(pi)t ?

The integral of tcos(pi)t is -(t^3)/3+C

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integral of tcos(pi)t

\int t cos (π) t d t

- \frac{t ^{3}}{3} + C

Solution steps

\int t cos (π) t d t

Take the constant out:

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

= cos (π) \cdot \int tt d t

cos (π) = - 1

= (- 1) \cdot \int tt d t

Simplify

tt : t^{2}

= (- 1) \cdot \int t^{2} d t

Apply the Power Rule

= (- 1) \frac{t ^{3}}{3}

Simplify

= - \frac{t ^{3}}{3}

Add a constant to the solution

= - \frac{t ^{3}}{3} + C

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