Calculus 3 - Double Integrals Over General Regions

∫∫(ax³ + by³ + sqrt(a²-x²) dA and
D = [-a,a] x [-b,b]

I can integrate it but my issue is that I don't know how how to visualize or graph [-a,a] x [-b,b] to start giving the integral the limits of integration.

Question

Calculus 3 - Double Integrals Over General Regions

∫∫(ax³ + by³ + sqrt(a²-x²) dA and 
D = [-a,a] x [-b,b]

I can integrate it but my issue is that I don't know how how to visualize or graph [-a,a] x [-b,b] to start giving the integral the limits of integration.

anonymous · Answer

you dont really need to visualize this since you are integrating over a region D, and region D is just a rectangle
so

$$\int\limits_{-a}^{a}\int\limits_{-b}^{b} ax^2 + by^3 + \sqrt{a^2 - x^2}  dydx $$

anonymous · Answer

Aha thank you. I forgot to read the a and b as just a constant

anonymous · Answer

your welcome glad to help