Solve it and u r genius

x
If f(x) is continuous function with ∫ f(t)dt →∞ as mod(x)→∞ then
0
show that every line y=mx intersects curve
x
y²+∫ f(t)dt =2
0

we need to prove that

x
y²+∫ f(t)dt =2 has a solution for y=mx
0
x
so that m²x²+∫ f(t)dt =2 is true! for some x
0

so that
x
∫ f(t)dt =2 - m²x² is true for some x
0

so that
x
∫ f(t)dt - 2 + m²x² = H(x)
0

has a root or H(x) = 0 at some x.
at x=0, the LHS is 0. RHS is 2

H(0) = -2

H(initnity ) tends to infinity

Hence. bye intermediate value theorem it iwll be zero for some x.

lol ..

Dont worry clear JEE with a good rank...

you will have genious written all over u :) ;) :P