double integral

Domain A is bounded by curve x² = 4y, ordinate x = 2, and x axis. The value of ∫∫A y dxdy is

If the value of the double integral $\int_{x=3}^{4}\int_{y=1}^{2}\frac{dydx}{(x+y)^2}$ is $\log_e (a/24)$, then $a$ is ________ (answer in integer).

If the value of the double integral $\int_{x=3}^{4} \int_{y=1}^{2} \frac{dydx}{(x + y)^2}$ is $\log_e(\frac{a}{24})$, then $a$ is __________ (answer in integer).

The value of $$\int\limits_C {\left[ {\left( {3x - 8{y^2}} \right)dx + \left( {4y - 6xy} \right)dy} \right],\,\,} $$ (where $$C$$ is the region bounded by $$x=0,$$ $$y=0$$ and $$x+...

The value of the integral $$\,\int\limits_0^2 {\int\limits_0^x {{e^{x + y}}\,\,dy} } $$ $$dx$$ is

By a change of variables $$x(u, v) = uv,$$ $$\,\,y\left( {u,v} \right) = {v \over u}$$ in a double integral, the integral $$f(x, y)$$ changes to $$\,\,\,f\left( {uv,{\raise0.5ex\hb...

Changing the order of integration in the double integral $${\rm I} = \int\limits_0^8 {\int\limits_{{\raise0.5ex\hbox{$\scriptstyle x$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\...