- #1
captainquarks
- 10
- 0
I am asked to consider the following graph:
r2=a+sin(θ), where a=2
I have a picture of this plot, which I have attached,
We are asked to find the area of the upper 'cresent' of the curve, contained at the top
How would I go about calculating that?
I've found that if I plot r=√(2+sinθ) and r=-√(2+sinθ) that this gives me the separate graphs individually, and that if I integrate from 0-π on the first one, then integrate from π-2π on the second one, if i subtract, i get the correct answer geometrically, using my graphing programme, but i don't know how to do this analytically? (i have attached another image to show the to sections - its the blue section i need)
Any help would be vastly appreciated, thank you
r2=a+sin(θ), where a=2
I have a picture of this plot, which I have attached,
We are asked to find the area of the upper 'cresent' of the curve, contained at the top
How would I go about calculating that?
I've found that if I plot r=√(2+sinθ) and r=-√(2+sinθ) that this gives me the separate graphs individually, and that if I integrate from 0-π on the first one, then integrate from π-2π on the second one, if i subtract, i get the correct answer geometrically, using my graphing programme, but i don't know how to do this analytically? (i have attached another image to show the to sections - its the blue section i need)
Any help would be vastly appreciated, thank you