Question

integration of {{ xy dydz = ?​

Answer 1

Given Integrand,

$\displaystyle \sf \iint xy \: dydz$

Firstly, we have to integrate the expression w.r.t y, needless to say 'x' is treated as a constant.

$\longrightarrow \displaystyle \sf \int \bigg(\int xy \: dy \bigg)dz \\ \\ \longrightarrow \displaystyle \sf \int x \bigg(\int y \: dy \bigg)dz \\ \\ \longrightarrow \displaystyle \sf \int x \bigg( \dfrac{ {y}^{1 + 1} }{ 1 + 1} \bigg)dz \\ \\ \longrightarrow \displaystyle \sf \dfrac{1}{2} \int x {y}^{2} dz$

We have to integrate the expression w.r.t z, xy² is treated as a constant.

$\longrightarrow \displaystyle \sf \dfrac{1}{2} {xy}^{2} \int dz \\ \\ \longrightarrow \displaystyle \sf \dfrac{1}{2} {xy}^{2} z + C$

Thus,

$\displaystyle \boxed{ \boxed{ \sf \iint xy \: dydz = \dfrac{1}{2} {xy}^{2} z + C}}$

Answer 2

The integration of {{ xy dydz = 1/2 xy²z+c

-Go through the attachment for the explanation.