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Area of a circle = 2r | ∫ | r | √( | 1 - | x^{2} | ) | dx |
-r | r^{2} |
1 - | x^{2} | = 1 - | (r • sin θ)^{2} | = 1 - | r^{2}•sin^{2}θ | = 1 - sin^{2}θ = cos^{2}θ |
r^{2} | r^{2} | r^{2} |
x = r • sin θ, | dx | = r • cos θ, dx = r • cos θ dθ |
dθ |
2r^{2} | ( | θ | + | sin(2θ) | ) | + C |
2 | 4 |
= r^{2} | ( | θ + | sin(2θ) | ) | + C |
2 |
1 - | x^{2} | = 1 - | (r • sin θ)^{2} | = 1 - | r^{2}•sin^{2}θ | = 1 - sin^{2}θ = cos^{2}θ |
r^{2} | r^{2} | r^{2} |
1 - | x^{2} | = cos^{2}θ |
r^{2} |
cos θ = | √( | 1 - | x^{2} | ) |
r^{2} |
θ = arcsin | ( | x | ) |
r |
sin θ = | x |
r |
cos θ = | √( | 1 - | x^{2} | ) |
r^{2} |
r^{2} | ( | θ + | sin(2θ) | ) | + C |
2 |
Have you found an error or do you want to add more
information to these pages? You can contact me at the bottom of the home page. |