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

The integral of x^2sin(y) is -x^2cos(y)+C

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integral of x^2sin(y)

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

- x^{2} cos (y) + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int sin (y) d y = - cos (y)

= x^{2} (- cos (y))

Simplify

= - x^{2} cos (y)

Add a constant to the solution

= - x^{2} cos (y) + C