Question

The area (in sq. units) of the region bounded by the curve $x^2=4y$ and the straight line $x=4y-2$:-

• A. $\frac{5}{4}$
• B. $\frac{9}{8}$
• C. $\frac{3}{4}$
• D. $\frac{7}{8}$

Answer 1

Answer: (B)

$\frac{9}{8}$

$x=4y-2$ & $x^2=4y$

$y=\frac{x+2}{4}$ and $y=\frac{x^2}{4}$

Solving the equations,
$\Rightarrow x^2=x+2\Rightarrow x^2-x-2=0$

$\therefore x=2,-1$

$\therefore$ Area of required line$=$Area of straight-line- area under a parabola

so, $\stackrel{2}{\underset{-1}{\int }}(\frac{x+2}{4}-\frac{x^2}{4})dx=\frac{9}{8}$