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can you give an example of where you have trouble at

so to get the other quadrants we have to be a bit more clever but not too much more

i understand everything except the pi

looking at your picture now

|dw:1437433116823:dw|

where R is
|dw:1437433154036:dw|

so are you asking how they got the limits ?

the limits of the angle yes

|dw:1437433287671:dw|

|dw:1437433324784:dw|

|dw:1437433373914:dw|

that is what they have in your picture
the top part of the circle

that is why they have theta is between 0 and pi

|dw:1437433484377:dw|

like does that answer your question?

but how do you see that it is in the second quadrant? and equals to pi?

well I drew it above

your R region is in the first quadrant and in the second quadrant

they gave us that we are suppose to look at these half top parts of x^2+y^2=1 and x^2+y^2=4

Well not reword the question
but give a slightly different question by rewording it

anyways I hope that did help
good luck

yes it's getting clearer and clearer now. thanks again!