Question
What is the area of the region enclosed by $$y = 2\left| x \right|$$ and $$y = 4\,?$$
A.
2 square units
B.
4 square units
C.
8 square units
D.
16 square units
Answer :
8 square units
Solution :
Required area $$ = 2\int\limits_{y = 0}^4 {\frac{y}{2}dy = } \left. {\frac{{{y^2}}}{2}} \right|_0^4 = \frac{{16}}{2} = 8\,{\text{sq}}{\text{. units}}$$
or, Area $$ = 2 \times 4 = 8\,{\text{sq}}{\text{. units}}$$
Required area $$ = 2\int\limits_{y = 0}^4 {\frac{y}{2}dy = } \left. {\frac{{{y^2}}}{2}} \right|_0^4 = \frac{{16}}{2} = 8\,{\text{sq}}{\text{. units}}$$
or, Area $$ = 2 \times 4 = 8\,{\text{sq}}{\text{. units}}$$