Have you tried making a sketch of this region?
Hello,
The problem is to convert a cartesian double integral to polar coordinates and evaluate. I'm fine with evaluating, I just require some assistance determining my bounds in polar coordinates
double integral f(x,y) = y and order of integration is dy dx
1< x< 2
0 < y < sqrt{4-(x^2)}
first of all, you need to determine the limits of your angle θ. since the region of integration is bounded below by the x-axis, one limit for θ is θ = 0.
the second limit will be the angle of the line through the origin and the point where the vertical line x = 1, and the semi-circle y = √(4 - x^2) intersect.
this should not be all that hard for you to deduce (it is a commonly encountered angle). the limits of r will depend on θ, you have two curves:
r = h1(θ), the vertical line x = 1, this will be the hard one to write down, and
r = h2(θ), the semi-circle y = √(4 - x^2). this should be obvious.
writing down f in polar coordinates will not be difficult, but don't forget the adjustment factor for dy dx.
what is the equation for a circle in polar coordinates? isn't it a really, really simple one?
for example, isn't the circle x^2 + y^2 = 1 just the constant function r = 1 in polar coordinates?
the equation for the vertical line is more challenging. see if you can put the fact that x = rcosθ to good use, if x is constant.