Let `A_n` be the area bounded by the curve `y=(tanx)^n` and the lines `x=0,y=0,` and `x=pi/4dot` Prove that for `n >2,A_n+A_(n-2)=1/(n-1)` and deduce `1/(2n+2)

If A_n be the area bounded by the curve y=(tanx)^n and the lines x=0,\ y=0,\ x=pi//4 , then for n > 2.

Let A_n be the area bounded by the curve y = x^n(n>=1) and the line x=0, y = 0 and x =1/2 .If sum_(n=1)^n (2^n A_n)/n=1/3 then find the value of n.

If the area bounded by the curve y=cos^-1(cosx) and y=|x-pi| is pi^2/n , then n is equal to…

If A_(n) is the area bounded by y=x and y=x^(n), n in N, then A_(2).A_(3)…A_(n)=

If I_n=int_0^(pi//4)tan^("n")x dx , prove that I_n+I_(n-2)=1/(n-1)dot

If A_n is the area bounded by y=x and y=x^n ,n in \mathbb{N} ,then A_2 A_3 ... A_n= (a) 1/(n(n+1)) (b) 1/(2^n n(n+1)) (c) 1/(2^(n-1)n(n+1)) (d) 1/(2^(n-2)n(n+1))

Prove that for ngt1 . int_0^1(cos^-1x)^ndx=n(pi/2)^(n-1)-n(n-1)int_0^1(cos^-1x)^(n-2)dx

If the polynomial equation a_n x^n + a_(n-1) x^(n-1) + a_(n-2) x^(n-2) + ....... + a_0 = 0, n being a positive integer, has two different real roots a and b . then between a and b the equation na_n x^(n-1) +(n-1)a_(n-1) x^(n-2) +.......+a_1 =0 has

Give first 3 terms of the sequence defined by a_n=n/(n^2+1)dot

Prove that the coefficients of x^n in (1+x)^(2n) is twice the coefficient of x^n in (1+x)^(2n-1)dot