Double Integrals sqrt(x^3+4) ...

[JJS]

I am stumped on how to even start these two double integrals (9a and 9b). Any help in the right direction would be greatly appreciated.

 

[Deleted member 4993]

I am stumped on how to even start these two double integrals (9a and 9b). Any help in the right direction would be greatly appreciated.

Your problem write up is too faint for me to decipher. Please write those - bigger - with black ink and re-post.

 

[JJS]

Better Upload

Here is a better scan. you can also click on the picture and zoom in. Thanks

 

[Prove It]

If you zoom in on the picture it is fine to read

Anyway, you have made a mistake in Question 6. As you have noted, there is a piece cut off. It would be better to use vertical strips in this case, instead of horizontal as you have tried. If you use horizontals then you need TWO separate integrals, as there are two different functions for the left hand boundary depending on where you are.

For both questions 9a and 9b, you need to reverse the order of integration.

 

[stapel]

For those who don't want to have to use two windows, here is the content from the second of the original poster's images:

\(\displaystyle \large{ \displaystyle \mbox{9a. }\, \int_0^{16}\, \int_{x\, =\, \sqrt{\strut y\,}}^{x\, =\, 4}\, \sqrt{\strut x^3\, +\, 4\,}\, dx\, dy }\)

\(\displaystyle \large{ \displaystyle \mbox{9b. }\, \int_0^{2}\, \int_{0}^{4\, -\, x^2}\, \dfrac{x\, e^{2y}}{4\, -\, y}\, dy\, dx }\)

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To the original poster:

You can typeset this stuff as:

9a. int[0, 16] int[x=sqrt(y), x=4] [ sqrt(x^3 + 4) ] dx dy

9b. int[0, 2] int[0, 4 - x^2] [ (x e^(2y)) / (4 - y) ] dy dx

For further information, please try this article on typing math as straight text. Thank you!