The question was to sketch the region of integration and readjust the order of integration.\$\$int^3_0 int^sqrt9-y_0 f(x,y) dxdy\$\$

When I lay out the region of integration I execute not view a means that it is possible to adjust the stimulate of integration. My an ar is bounded by, \$y=3\$, \$y=0\$, \$x=0\$ and \$x=sqrt9-y\$.Any insight would help, if over there is a method to perform this then i guess I have it sketched wrong.My image is listed below of what i drew

You are watching: Sketch the region of integration and change the order of integration

\$egingroup\$ looking at your sketch, you should be able to see that this is a simple region. So what room the limit on \$x\$? Both of castle will need to be constants, so what space the excessive values the \$x\$ in your graph? Then number out the bounds on \$y\$. At the very least one of them would must be a role of \$x\$. \$endgroup\$
The integration is performed over the region where \$0le yle3\$ and \$0le xlesqrt9-y\$. This is the region shown below

So to readjust the order of integration, we need to define the upper \$x\$ border by a piecewise duty or compose the integral as the sum of 2 integrals:

\$\$int_0^sqrt6int_0^3f(x,y), astecraftedmcd.comrmdy, astecraftedmcd.comrmdx+int_sqrt6^3int_0^9-x^2f(x,y), astecraftedmcd.comrmdy, astecraftedmcd.comrmdx\$\$

Try to express y in regards to x, and also then figure out what that way about the limit of x, which end up being constants.

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