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`

If f, is a continuous function with int_(0)^(x)f(t)dt rarr oo as |x|->oo then show that every line y=mx intersects the curve y^(2)+int_(0)^(x)f(t)dt=2

If a continuous function f satisfies int_(0)^(f(x))t^(3)dt=x^(2)(1+x) for all x>=0 then f(2)

Let f:[0,oo)rarrR be a continuous function such that f(x)=1-2x+int_(0)^(x)e^(x-t)f(t)dt" for all "x in [0, oo). Then, which of the following statements(s) is (are)) TRUE?

If f(t) is a continuous function defined on [a,b] such that f(t) is an odd function, then the function phi(x)=int_(a)^(x) f(t)dt

Let f(x) be an odd continuous function which is periodic with period 2. if g(x)=int_(0)^(x) f(t)dt , then

A continuous function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt then f(1)=

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