Area Under Curves Question 2
Question 2 - 24 January - Shift 2
If the area of the region bounded by the curves
$y^{2}-2 y=-x, x+y=0$ is $A$, then $8 A$ is equal to
Show Answer
Answer: 36
Solution:
Formula: Area between two curves - Area enclosed between two curves intersecting at two different points
$y^{2}-2 y=-x$
$\Rightarrow y^{2}-2 y+1=-x+1$
$(y-1)^{2}=-(x-1)$
$y=-x$
Points of intersection
$x^{2}+2 x=-x$
$x^{2}+3 x=0$
$x=0,-3$
$A=\int_0^{3}(-y^{2}+2 y+y) d y$
$=[\frac{3 y^{2}}{2}-\frac{y^{3}}{3}]_0 ^{3}=\frac{9}{2}$
$8 A=36$
