(sin^(-1)x)^(m)

If m and M are the least and the greatest value of (cos^(-1)x)^(2)+(sin^(-1)x)^(2) , then (M)/(m) is equal to

((sin^(m)x)/(sin^(n)x))^(m+n)*((sin^(n)x)/(sin^(q)x))^(n+q)((sin^(q)x)/(sin^(m)x))^(q+m)

If quad ((sin^(m)x)/(sin^(n)x))^(m+n)((sin^(n)x)/(sin^(p)x))^(n+p)((sin^(p)x)/(sin^(m)x))^(p+) then f(x) is equal to

If M and m are the greatest and least value of the function f(x)=(cos^(-1)x)^2+(sin^(-1)x)^2 then the value of ((M+9m)/m)^3 is …..

If M and m are the greatest and least value of the function f(x)=(cos^(-1)x)^2+(sin^(-1)x)^2 then the value of ((M+9m)/m)^3 is …..

If m, n in N , then int_(0)^(pi//2)((sin^(m)x)^(1/n))/((sin^(m)x)^(1/n)+(cos^(m)x)^(1/n))dx is equal to

If m, n in N , then int_(0)^(pi//2)((sin^(m)x)^(1/n))/((sin^(m)x)^(1/n)+(cos^(m)x)^(1/n))dx is equal to

If f(x) = sin^(-1)(m^(2) -3m+ 1)sec (absx)/3-[e^(m-4)](sin{x}) , where {} denotes fractional part of x. If f(x) if f(x) is periodic, then number of possible integral values of m is

Prove : int sin mx sin n x dx[ m^(2) != n^(2)] , = 1/2 [ (sin(m-n)x)/(m-n) - (sin (m+n)x)/(m+n) ] + c

Differentiate sin(m\ sin^(-1)x) with respect to x :