Area Under Curves Question 1
Question 1 - 24 January - Shift 1
The area enclosed by the curves $y^{2}+4 x=4$ and $y-2 x=2$ is :
(1) $\frac{25}{3}$
(2) $\frac{22}{3}$
(3) 9
(4) $\frac{23}{3}$
Show Answer
Answer: (3)
Solution:
Formula: Area between two curves - Area enclosed between two curves intersecting at two different points
$y^{2}+4 x=4$
$y^{2}=-4(x-1)$
$A=\int _{-4}^{2}(\frac{4-y^{2}}{4}-\frac{y-2}{2}) d y$
$\begin{aligned} & =\left[2 y-\frac{y^3}{12}-\frac{y^2}{4}\right]_{-4}^2 \\ & =\left(4-\frac{2}{3}-1\right)-\left(-8+\frac{16}{3}-4\right) \\ & =3+12-\frac{18}{3} \\ & =15-6 \\ & =9\end{aligned}$
So, the correct option is (3)
