Home
Class 12
MATHS
A function f, continuous on the positive...

A function f, continuous on the positive real axis, has the property that for all choices of x gt 0 and y gt 0, the integral `int_(x)^(xy)f(t)dt` is independent of x (and therefore depends only on y). If f(2) = 2, then `int_(1)^(e)f(t)dt` is equal to

Promotional Banner

Similar Questions

Explore conceptually related problems

If f(t) is an odd function, then int_(0)^(x)f(t) dt is -

lim_(x to 0)(int_(-x)^(x) f(t)dt)/(int_(0)^(2x) f(t+4)dt) is equal to

lim_(x to 0)(int_(-x)^(x) f(t)dt)/(int_(0)^(2x) f(t+4)dt) is equal to

Let g(x) = int_(x)^(2x) f(t) dt where x gt 0 and f be continuous function and 2* f(2x)=f(x) , then

int_(0)^( If )(f(t))dt=x+int_(x)^(1)(t^(2)*f(t))dt+(pi)/(4)-1 then the value of the integral int_(-1)^(1)(f(x))dx is equal to

If" f, is a continuous function with int_0^x f(t) dt->oo as |x|->oo then show that every line y = mx intersects the curve y^2 + int_0^x f(t) dt = 2