Question

Anybody know the integration for this... The answer is k=3

Answer 1

You know that
`y^2=4x` so
`x=(y^2)/(4)`.
Area of a shaded region is:


`$A=\int\limits_0^k(y^2)/(4)\,dy=(1)/(4)\int\limits_0^ky^2\,dy=(1)/(4)\left[(y^3)/(3)\right]_0^k=(1)/(4)\left[(k^3)/(3)-(0^3)/(3)\right]=(1)/(4)\cdot(k^3)/(3)=\boxed{(k^3)/(12)}`

so k:


`(k^3)/(12)=(9)/(4)\\\\\\k^3=(9\cdot12)/(4)\\\\\\k^3=9\cdot3\\\\k^3=3^3\quad|\sqrt[3]{(\ldots)}\\\\\boxed{k=3}`