The area (in sq. units) of the region bounded by

Question:

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

x = 4y – 2 :- 

  1. $\frac{5}{4}$

  2. $\frac{9}{8}$

  3. $\frac{3}{4}$

  4. $\frac{7}{8}$


Correct Option: , 2

Solution:

$x=4 y-2 \& x^{2}=4 y$

$\Rightarrow x^{2}=x+2 \Rightarrow x^{2}-x-2=0$

$x=2,-1$

So, $\int_{-1}^{2}\left(\frac{x+2}{4}-\frac{x^{2}}{4}\right) d x=\frac{9}{8}$

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