[x=int4''-3n-1:n in N2arcl y=int theta(n-1):nc pi],[" then "xuy" ecuad "]

If f (n)= 1/pi int _(0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2) theta), n in N, then evulate (f (15)+ f (3))/( f (12) -f (10)).

If f (n)= 1/pi int _(0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2) theta), n in N, then evulate (f (15)+ f (3))/( f (12) -f (10)).

If the line x cos theta+y sin theta=P is the normal to the curve (x+a)y=1, then show theta in(2n pi+(pi)/(2),(2n+1)pi)uu(2n pi+(3 pi)/(2),(2n+2)pi),n in Z

If u_(n)=int_(0)^((pi)/(2))theta sin^(n)theta d theta and n>=1, then prove that u_(n)=((n-1)/(n))u_(n-2)+(1)/(n^(2))

int_n^(n+1)f(x) dx=n^2+n then int_(-1)^1 f(x) dx =

If I_n = int_0^(pi//4) tan^n theta d theta , then for any +ve integer n, the value of n(I_(n - 1) + I_(n + 1)) is :

int_(0)^(x)[sin t]dt, where x in(2n pi,(2n+1)pi),n in N, and [.] denotes the greatest integer function is equal to -n pi(b)-(n+1)pi2n pi(d)-(2n+1)pi