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# Curls : Green's Theorem

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When I write A_n it means A "sub" n.

a) Define A_n= integral from 2pi to 0 of (Cos(theta))^(2n).d(theta)

Proove the recurrence formula(*):

A_n=(2n-1)/(2n)*A_(n-1)

by writing Green's thorem for vector field F=x^(2n-1)j in the unit disc x^2+y^2<1 and evaluating each of the integrals separately. ( Use polar coordinates)

b) Compute A_0 and derive,using (*), the formula for A_n. (remember the integrals there are from 0 to Pi/2, not 2pi.)

##### Solution Summary

Curls are investigated using Green's theorem. Separated integrals are examined.

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