Question

Need help! How to solve elliptic function ?

Answer 1

\[\int\limits_{0}^{\pi/4}\frac{ d \phi }{ \sqrt{1-0.25 \sin ^{2} \phi} }\]

Answer 2

@oldrin.bataku can you help me ?

Answer 3

elliptic integral of the first kind

Answer 4

\[F(k,\phi) = \int\limits_{0}^{\phi} \frac{d\theta}{\sqrt{1 - k^2 \sin^2 \theta}}\]\[0<k<1\]

Answer 5

\[\int\limits_{0}^{\frac{\pi}{4}} \frac{d\phi}{\sqrt{1 - 0.25\sin^2 \phi}}=F(\frac{1}{2},\frac{\pi}{4})\]

Answer 6

that's the answer in terms of incomplete elliptic integral of first kind

Answer 7

then..., how about in terms of value ??

Answer 8

\[F(\frac{ 1 }{ 2 } , \frac{ \pi }{ 4 } ) = ?\]

Answer 9

I am afraid there's no exact value for elliptic integrals

Answer 10

ok..., then how about
\[\int\limits_{-1/2}^{3/4} \sqrt{\frac{ 9-4x^{2} }{ 1-x^{2} }} dx\]
the answer in answer key is 3.96.
can you help me ?

Answer 11

this is an elliptic integral too, but you don't need to find the exact value

Answer 12

you just need to approximate it

Answer 13

ok.., how to do it ??

Answer 14

is this problem from numerical analysis/numerical methods?

Answer 15

hmm.., i dont know., but how to approximate it without using 'programming' ??

Answer 16

well if you see here, the indefinite integral of the function is not elementary

http://www.wolframalpha.com/input/?i=integrate+sqrt%28%289+-+4x%5E2%29%2F%281+-+x%5E2%29%29

Answer 17

a graphing calculator will approximate the area under curve for you
by hand you have to use a summation:
\[\int\limits_{a}^{b}f(x) dx \approx \sum_{i=0}^{n} f(x_i) *dx\]
where dx is step size..smaller dx the more accurate the approximation

Answer 18

or maybe the trapezoidal rule\[\int\limits_{a}^{b} f(x) \: dx = \frac{b - a}{n}\left(f(x_0)+2f(x_1)+2f(x_2)+...+2f(x_{n-1})+f(x_n)\right)\]

Answer 19

@whpalmer4 can you help on this person?