JEE Advance - Mathematics (1991 - No. 25)
If $$'f$$ is a continuous function with $$\int\limits_0^x {f\left( t \right)dt \to \infty } $$ as $$\left| x \right| \to \infty ,$$ then show that every line $$y=mx$$
intersects the curve $${y^2} + \int\limits_0^x {f\left( t \right)dt = 2!} $$
intersects the curve $${y^2} + \int\limits_0^x {f\left( t \right)dt = 2!} $$
intersects the curve at exactly one point
intersects the curve at at least two points
intersects the curve at at least one point
does not intersect the curve
intersects the curve at infinitely many points