NCERT Solutions - Exercise 8.1 : Application of Integral

Application of Integral

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 x-axis and y-axis.

∴ 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 x-axis and y-axis.

∴ 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 x²  +  y² = 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 y² = 4x, y-axis and the line y = 3 is

A. 2 

B. 

C. 

D. 

ANSWER : - The area bounded by the curve, y² = 4x, y-axis, and y = 3 is represented as

Thus, the correct answer is B.