Find the domain of the real valued function `f(x)=sqrt((x-alpha)(beta-x)),(theta lt alpha lt beta)`.

Integrate : int (dx)/(sqrt((x-alpha)(beta-x)))[ alpha lt x lt beta]

Evaluate the following intergrals : int sqrt((x-alpha)(beta-x))dx(alpha lt x lt beta)

Let f(x) be a differentiable function and f(alpha)=f(beta)=0(alpha

Let f(x) be a differentiable function and f(alpha)=f(beta)=0(alpha< beta), then the interval (alpha,beta)

The maximum possible integral value of (beta-alpha)/(tan^(-1)beta - tan^(-1)alpha , where 0lt alpha lt beta lt sqrt3 , is

The maximum possible integral value of (beta-alpha)/(tan^(-1)beta - tan^(-1alpha) , where 0lt alpha lt beta lt sqrt3 , is

The maximum possible integral value of (beta-alpha)/(tan^(-1)beta - tan^(-1alpha) , where 0lt alpha lt beta lt sqrt3 , is

The value of int_(alpha)^(beta) x|x|dx , where a lt 0 lt beta , is

The value of int_(alpha)^(beta) x|x|dx , where a lt 0 lt beta , is

Find the domain of f(x)=cos^-1(sqrt(x^2-x+1))/(sqrt(sin^-1((2x-1)/2)) is the integral (alpha,beta] then alpha+beta