Book: RD Sharma - Mathematics (Volume 2)
Chapter: 21. Areas of Bounded Regions
Subject: Maths - Class 12th
Q. No. 13 of Exercise 21.1
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
Determine the area under the 
included between the lines x = 0 and x = 1
Given equations are :
...... (1)
x = 0 (y – axis)
x = 1 (represents a line parallel to y - axis at a distance 1 to the right)
equation (1) represents a half eclipse that is symmetrical about the x - axis and also about the y - axis with center at origin.
A rough sketch is given as below: -
We have to find the area of shaded region.
Required area
= (shaded region OABCO)
(the area can be found by taking a small slice in each region of width Δx, then the area of that sliced part will be yΔx as it is a rectangle and then integrating it to get the area of the whole region)
(As x is between (0,1) and the value of y varies)
(as 
)
Substitute 
So the above equation becomes,
We know, 
So the above equation becomes,
Apply reduction formula:
On integrating we get,
Undo the substituting, we get
On applying the limits we get,
Hence the area under the 
included between the lines x = 0 and x = 1 is equal to
square units.
