This qsn came in FIITJEE AITS 2day.
I_n=\int_{\frac{\pi}{2}}^{\propto}{e^{-x}cos^{n}xdx}=\frac{720}{3145}e^{-\frac{\pi}{2}}
This holds for n=2m, where m is a natural number. Find it.
1yeah tis q is gud the soln is quite gud...rare in fiitjee soln
@soumik pls see fiitjee propability n matrices
66That's incorrect. The correct recurrence is
I_n =\dfrac{n(n-1)}{n^2+1}I_{n-2}
and obviously
I_0=e^{-\pi/2}
So that
I_2=\dfrac{2}{5}e^{-\pi/2}
I_4=\dfrac{24}{85}e^{-\pi/2}
And
I_6=\dfrac{144}{629}e^{-\pi/2}=\dfrac{720}{3145}e^{-\pi/2}
Accordingly
\boxed{m=3}
1no sir m=6
we get it by applying by parts 2 times
the recurrence is correct as u have said
we get
n!Io
In = ---------------------------------------------------
(1+n^2)(1+(n-2)^2)....(1+2^2)
