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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