2.Sketch the region whose area is given by the integral and evaluate the integral. 3.Evaluate the given integral by changing to polar coordinates.

2. The integration region,

corresponds to what you might call an "annular sector" (i.e. the analog of circular sector for the annulus or ring). In other words, it's the region between the two circles of radii and , taken between the rays and . (The previous question of yours that I just posted an answer to has a similar region with slightly different parameters.)

You can separate the variables to compute the integral:

which should be doable for you. You would find it has a value of 19/72*(3√3 + 4π).

3. Without knowing the definition of the region D, the best we can do is convert what we can to polar coordinates. Namely,

so that

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb