Applications Of Integrals

The given curve is




This is the equation of the ellipse having centre ( ,0 ).
Observe the figure of ellipse (1). The centre P is ( ,0 ). A and B are and
respectively.
The required area = 4 ? area of figure PQB
ydx
dx
dx




=4 square units.

Step 1: Find the equation of the lines.
The equation is a linear equation. We compute the area of the region enclosed by the lines by integrating between and .
Step 2: Conclusion.
The area is 14 square units.
Final Answer:

Required area

s units