What is the integral of y^2sin(n)y ?

The integral of y^2sin(n)y is 1/4 y^4sin(n)+C

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integral of y^2sin(n)y

\int y^{2} sin (n) y d y

\frac{1}{4} y^{4} sin (n) + C

Solution steps

\int y^{2} sin (n) y d y

Take the constant out:

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

= sin (n) \cdot \int y^{2} y d y

Simplify

y^{2} y : y^{3}

= sin (n) \cdot \int y^{3} d y

Apply the Power Rule

: \frac{y ^{4}}{4}

= sin (n) \frac{y ^{4}}{4}

Simplify

sin (n) \frac{y ^{4}}{4} : \frac{1}{4} y^{4} sin (n)

= \frac{1}{4} y^{4} sin (n)

Add a constant to the solution

= \frac{1}{4} y^{4} sin (n) + C

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