Question

Find the area

Answer 1

The area (in sq. units ) of the region described by
\(\large \color{black }{\begin{align}\{(x,y):y^2\leq 2x \quad \text{ and }\quad y\geq 4x-1\}
\end{align}}\)

is


\(\large \color{black }{\begin{align}&(1.)\quad \dfrac{15}{64}\hspace{.33em}\\~\\
&(2.)\quad \dfrac{9}{32}\hspace{.33em}\\~\\
&(3.)\quad \dfrac{7}{32}\hspace{.33em}\\~\\
&(4.)\quad \dfrac{5}{64}\hspace{.33em}\\~\\\end{align}}\)

Answer 2

Start by finding out which equation is 'on top of' the other equation, it is likely the linear one, and then you need to perform an integration, this is because the integral is the area under a curve.

If you integrate the one higher, and the intrgate the lower one, and subtract the difference, you find the area between them :)

Answer 3

also it would be better if u take y as the independent variable