Question 1: Find the area of the region bounded by the ellipse
ANSWER :  The given equation of the ellipse, , can be represented as
It can be observed that the ellipse is symmetrical about xaxis and yaxis.
∴ Area bounded by ellipse = 4 × Area of OAB
Therefore, area bounded by the ellipse = 4 × 3π = 12π units
Question 2: Find the area of the region bounded by the ellipse
ANSWER : The given equation of the ellipse can be represented as
It can be observed that the ellipse is symmetrical about xaxis and yaxis.
∴ Area bounded by ellipse = 4 × Area OAB
Therefore, area bounded by the ellipse =
Question 3: Area lying in the first quadrant and bounded by the circle x^{2} + y^{2} = 4 and the lines x = 0 and x = 2 is
A. π
B.
C.
D.
ANSWER : The area bounded by the circle and the lines, x = 0 and x = 2, in the first quadrant is represented as
Thus, the correct answer is A.
Question 4: Area of the region bounded by the curve y^{2} = 4x, yaxis and the line y = 3 is
A. 2
B.
C.
D.
ANSWER :  The area bounded by the curve, y^{2} = 4x, yaxis, and y = 3 is represented as
Thus, the correct answer is B.
209 videos443 docs143 tests

1. What is the application of integrals? 
2. How do integrals help in finding areas? 
3. Can integrals be used to determine the volume of irregular shapes? 
4. What are the reallife applications of integrals? 
5. How are integrals used in optimization problems? 
209 videos443 docs143 tests


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