What is the Correct Domain of Integration for a Double Integral Problem?

[synergix]

Homework Statement

question 2:
http://www.math.ubc.ca/~haber/courses/math253/Welcome_files/asgn5.pdf"

The Attempt at a Solution

So for part a) I tried to plot my domain of integration and ended up concluding it was an area bounded by y=0, y=4-x^2, and x=1. Is this okay?

In not too sure about part b) I'm just going off the graph here and so if that's wrong this will be wrong. Here is what i did I changed x domain from 1->(4-x^2) to 1->2 and I changed y domain from 0->3 to 0->4-x^2.

Is this correct?

Thanks!

 

[synergix]

how could we integrate when the upper bound of the first integral is a polynomial x=4-x^2? Maybe I am misunderstanding something. Would it not have to be either a constant or a function of y?

 

[LCKurtz]

The upper limit on the inner integral is surely a typo and probably is supposed to be x = 4 - y².

 

[synergix]

I sure hope so. Thank you.