If `A=int_0^1 x^(50)(2-2x)^(50)dx ,B=int_0^1 x^(50)(1-x)^(50)dx ` , which of the following is true? (A) `A=2^(50)B` (B) `A=2^(-50)B` (C) `A=2^(100)B` (D) `A=2^(-100)B`

Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)

If int_0^1 xe^(x^2) dx=k int_0^1 e^(x^2) dx , then (A) kgt1 (B) 0ltklt1 (C) k=1 (D) none of these

int_(0)^(50pi)| cos x|dx=

Evaluate I(b)=int_(0)^(1)(x^(b))dx=int_(0)^(1)(x^(b)-1)/("ln"x)dx,bge0 .

Which of the following holds true? (A) 101^50-100^50gt99^50 (B) 101^50-99^50lt100^50 (C) (1000)^1000gt(1000)^999 (D) (10001)^999lt(1000)^1000

If A_n=int_0^(pi/2)(sin(2n-1)x)/(sinx)dx ,B_n=int_0^(pi/2)((sinn x)/(sinx))^2 dx for n inN , Then (A) A_(n+1)=A_n (B) B_(n+1)=B_n (C) A_(n+1)-A_n=B_(n+1) (D) B_(n+1)-B_n=A_(n+1)

In the expansion of (1+x)^50 the sum of the coefficients of odd power of x is (A) 0 (B) 2^50 (C) 2^49 (D) 2^51

int_0^2 x^3[1+cos((pix)/2)]dx , where [x] denotes the integral part of x , is equal to (A) 1/2 (B) 1/4 (C) 0 (D) none of these

int_0^1 [x^2-x+1]dx , where [x] denotes the integral part of x , is (A) 1 (B) 0 (C) 2 (D) none of these

Evaluate : int_0^oo1/(a^2+b^2x^2)dx