What is the integral of t^2sin(θ)t ?

The integral of t^2sin(θ)t is 1/4 t^4sin(θ)+C

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integral of t^2sin(θ)t

\int t^{2} sin (θ) t d t

\frac{1}{4} t^{4} sin (θ) + C

Solution steps

\int t^{2} sin (θ) t d t

Take the constant out:

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

= sin (θ) \cdot \int t t^{2} d t

Simplify

t t^{2} : t^{3}

= sin (θ) \cdot \int t^{3} d t

Apply the Power Rule

: \frac{t ^{4}}{4}

= sin (θ) \frac{t ^{4}}{4}

Simplify

sin (θ) \frac{t ^{4}}{4} : \frac{1}{4} t^{4} sin (θ)

= \frac{1}{4} t^{4} sin (θ)

Add a constant to the solution

= \frac{1}{4} t^{4} sin (θ) + C

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What is the integral of t^2sin(θ)t ?
The integral of t^2sin(θ)t is 1/4 t^4sin(θ)+C