Question

Area bounded by $y^2=4x,X-$axis and tangent drawn to $y^2=4x$ at $(1,2)$ is

• A. $\frac{5}{16}$
• B. $\frac{4}{3}$
• C. $\frac{2}{3}$
• D. $\frac{3}{4}$

Answer 1

The correct option is C $\frac{2}{3}$

We have,

$y^2=4x$

On differentiating w.r.t $x$, we get

$2y\frac{dy}{dx}=4\frac{dy}{dx}\left(1,2\right)=1$

Since, $y=mx+c$

Therefore,

$y=x+c2=1+cc=1$

So,

$y=x+1$

Therefore,

$Area={\int }_{-1}^1\left(x+1\right)dx-2{\int }_0^1\sqrt{x}dx={\left[\frac{x^2}{2}+x\right]}_{-1}^1-\frac{4}{3}{\left[x^{3/2}\right]}_0^1=2-\frac{4}{3}=\frac{2}{3}Ans.$