If `I_(1)=int_(0)^(1)(1-x^(50))^(100)dx` and `I_(2)=int_(0)^(1)(1-x^(50))^(101)dx,` If `I_(2)=(alpha)/(beta)I_(1)` (`alpha,beta` are coprime) then `beta-alpha`

Evaluate: 5050(int_(0)^(1)(1-x^(50))^(100)dx)/(int_(0)^(1)(1-x^(50))^(101)dx)

The value of ((5050)int_(0)^(1)(1-x^(50))^(100)dx)/(int_(0)^(1)(1-x^(50))^(101)dx) is

Let I_1= int_0^1 (1-x^50)^100 dx and I_2= int_0^1(1-x^50)^101 dx and I_1= lamda I_2 , then lamda is

If I_(1)=int_(0)^( pi/2)(sin x)^(sqrt(3)+1)dx,I_(2)=int_(0)^(pi/2)(sin x)^(sqrt(3)-1))dx then (I_(1))/(I_(2))=

If I_(1)=int_(0)^(1) 2^(x^(2)) dx, I_(2)=int_(0)^(1) 2^(x^(3)) dx, I_(3)=int_(1)^(2) 2^(x^(2))dx and I_(4)=int_(1)^(2) 2^(x^(2))dx then

Let I_(1)=int_(0)^(alpha)(1+2cosx)/(1+e^(x))dx and I_(2)=int_(0)^(alpha)(1+e^(x))/(1+2cosx)dx , where alpha is the root of the equation 2 cos x - e^(x)=0 . and alpha is positive Then,

int(x backslash dx)/(root(2 0 0 1 2)((1+x^(2))^(1012)(2+x^(2))^(3012)))=(alpha)/(2 beta)(1-f(x))^(beta/ alpha)+c

Let int_(alpha)^( beta)(f(alpha+beta-x))/(f(x)+f(alpha+beta-x))dx=4 then

Let I_(n)= int_(1)^(e ) x^(19) (log|x|)^(n)dx , where n in N . If (20)I_(10)=alpha I_(9)+betaI_(8) , for natural numbers alpha and beta , then alpha-beta equals to ________.

Evaluate: int(1)/((x-alpha)(beta-x))dx,(beta>alpha)