Question

solve the following question with step by step.

∫∫ 2xy dxdy

Answer 1

$\large\iint2xy\,dx\,dy$ =

$\large\int(\int2xy\,dy)dx$ =

$\large\int((2\times x\times\dfrac{y^{1+1}}{2})+c_1)dx$ =

$\large\int (xy^2+c_1)dx$ =

$\large\int xy^2+c_1\,\,dx$ =

$\large\int xy^2\,dx+\int c_1\,dx$ =

$\large(\int xy^2\,dx)+(c_1\int dx)$ =

$\large(\dfrac{x^{1+1}}{2} \times y^2 ) +(c_1\times x) + c_2$ =

$\large\dfrac{x^2y^2}{2} \, + c_1x+c_2$