Question

integration help

Answer 1

May I help?

Answer 2

\[y=\frac{ 1 }{ \sqrt{8} }x^2 ...(1)\]
\[y=\sqrt{x} ...(2)\]
from (1) and (2)
\[\sqrt{x}=\frac{ 1 }{ \sqrt{8} }x^2\]
squaring
\[x=\frac{ x^4 }{ 8 },x^4=8x,x^4-8x=0\]
\[x(x^3-8)=0,x=0 \]
\[x^3-8=0,x^3=8=2^3,x=2\]
when x=0,y=0
when x=2
\[y=\sqrt{2}\]
so point of intersection is \[\left( 0,0 \right)~and~\left( 2,\sqrt{2} \right)\]

Answer 3

\[reqd. area=\int\limits_{0}^{2}\left[ \sqrt{x}-\frac{ 1 }{ \sqrt{8} }x^2 \right]dx\]
can you complete it?