Multiple integrals

**sajjad002** · May 25th 2009, 09:49 PM

Question # 01:

Evaluate the iterated integral by converting to polar coordinates

The region of integration is bounded by

Question # 02:

Evaluate the triple integral

**matheagle** · May 25th 2009, 09:58 PM

The first is just $\int_{-\pi/2}^{\pi/2}\int_0^2 re^{r^2}dr d\theta =\pi\int_0^2 re^{r^2}dr$ .

WHERE I think you have $x^2+y^2$ in the exponent of e, but IT's hard to read.

Now integrate with $u=r^2$ .

**sajjad002** · May 25th 2009, 10:01 PM

Originally Posted by matheagle

the first is just $\int\int re^{r^2}dr d\theta$

WHERE I think you have $x^2+y^2$ in the exponent of e, but IT's hard to read.

$\int_{-0}^{2}\int_{-(4-x^2)^{1/2}}^{(4-x^2)^{1/2}} e^{-x^2-y^2}dy dx$

**matheagle** · May 25th 2009, 10:08 PM

The second one is

$\int_2^3dx\int_{-1}^1\int_0^1 (\sqrt{y}-3z^2)dydz=\int_{-1}^1\int_0^1(\sqrt{y}-3z^2)dydz$ .

$=\int_{-1}^1((2/3)y^{3/2}-3z^2y)\biggr|_{y=0}^{y=1}dz=\int_{-1}^1((2/3)-3z^2)dz$ ....

**CaptainBlack** · May 25th 2009, 11:13 PM

Originally Posted by matheagle

????????????

Try quoting the post if its unreadable due to latex errors, at least you will then see what the post contained, and you would not leave the rest of us wondering what you are refering to.

CB

**matheagle** · May 25th 2009, 11:53 PM

I've done that before, but I was too tired and didn't think of doing that tonight.

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