# Step-by-step Solution

## Trigonometric integral int(cos(y)*(1/2)*y^2)dy

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### Videos

$\frac{1}{2}y^2\sin\left(y\right)-\left(-y\cos\left(y\right)+\sin\left(y\right)\right)+C_0$

## Step-by-step explanation

Problem to solve:

$\:\int\left(cos\:y\right)\cdot\frac{1}{2}y^2dy$
1

Take the constant out of the integral

$\frac{1}{2}\int y^2\cos\left(y\right)dy$
2

Use the integration by parts theorem to calculate the integral $\int y^2\cos\left(y\right)dy$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

$\frac{1}{2}y^2\sin\left(y\right)-\left(-y\cos\left(y\right)+\sin\left(y\right)\right)+C_0$
$\:\int\left(cos\:y\right)\cdot\frac{1}{2}y^2dy$

### Main topic:

Trigonometric integrals

~ 1.22 seconds