Solve ∫ x^2sin(y) wrt y

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

Evaluate

$$-x^{2}\cos(y)+С$$

Solution Steps

Factor out the constant using \int af\left(y\right)\mathrm{d}y=a\int f\left(y\right)\mathrm{d}y.

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

Use \int \sin(x)\mathrm{d}x=-\cos(x) from the table of common integrals to obtain the result.

$$-x^{2}\cos(y)$$

If F\left(y\right) is an antiderivative of f\left(y\right), then the set of all antiderivatives of f\left(y\right) is given by F\left(y\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$-x^{2}\cos(y)+С$$

Differentiate w.r.t. x

$$-2x\cos(y)$$