The questions asks:
"Let R be the region in the first quadrant bounded by the graphs of the parabolas $y=2x^2$, $y=9-x^2$ and the line x=0. Express the area of region R:
(i) Integrating first with respect to y, and then with respect to x
(ii) Integrating first with respect to x, and then with respect to y "
I have tried sketching the two curves, and expressing the double integral. However, my sketch and the double integral itself is quite different from the solution. Please have a look at my attempt and the solution below:
Could someone please help me understand this solution? I feel like I am missing a very important concept about double integrals. Any help would be highly appreciated.