what would the limit be in this problem?

Question

Determine the volume of the solid lying under the graph of
z= 2x+y and above the bounded region enclosed by the graphs of y^2=x and y= x^2

are the limits from x to y^2 and from x^2 to y?

Answer 1

I assume you are using a double integral to solve this?
The limits on each integral must be in terms of the variable you are integrating with respect to.

If you start by first integrating with respect to y, your lower limit should be x^2. You get the upper limit by solving for y in the equation y^2 = x. Solving for y gives you y = ± √x. The border of the region that is enclosed is along y = +√x. So the upper limit is √x.
Then you can integrate with respect to x from 0 to 1.

Alternatively, you can integrate with respect to x first. Solve your equations for x instead to get your limits.