Find the best tutors and institutes for Class 12 Tuition
Search in
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
The area of the region bounded by the curve, y2 = x, the lines, x = 1 and x = 4, and the x-axis is the area ABCD.
Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.
The area of the region bounded by the curve, y2 = 9x, x = 2, and x = 4, and the x-axis is the area ABCD.
Find the area of the region bounded by x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant.
The area of the region bounded by the curve, x2 = 4y, y = 2, and y = 4, and the y-axis is the area ABCD.
Find the area of the region bounded by the ellipse 
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
Find the area of the region bounded by the ellipse 
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 = 
Find the area of the region in the first quadrant enclosed by x-axis, line 
and the circle 
The area of the region bounded by the circle, 
, and the x-axis is the area OAB.
The point of intersection of the line and the circle in the first quadrant is 
.
Area OAB = Area ΔOCA + Area ACB
Area of OAC 
Area of ABC 
Therefore, required area enclosed = 3√2 + π3 − 3√2 = π3 square units
Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line 
The area of the smaller part of the circle, x2 + y2 = a2, cut off by the line, , is the area ABCDA.
It can be observed that the area ABCD is symmetrical about x-axis.
∴ Area ABCD = 2 × Area ABC
Therefore, the area of smaller part of the circle, x2 + y2 = a2, cut off by the line, , is 
units.
The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.
The line, x = a, divides the area bounded by the parabola and x = 4 into two equal parts.
∴ Area OAD = Area ABCD
It can be observed that the given area is symmetrical about x-axis.
⇒ Area OED = Area EFCD
From (1) and (2), we obtain
Therefore, the value of a is 
.
Find the area of the region bounded by the parabola y = x2 and 
The area bounded by the parabola, x2 = y,and the line,, can be represented as
The given area is symmetrical about y-axis.
∴ Area OACO = Area ODBO
The point of intersection of parabola, x2 = y, and line, y = x, is A (1, 1).
Area of OACO = Area ΔOAM – Area OMACO
Area of ΔOAM 
Area of OMACO 
⇒ Area of OACO = Area of ΔOAM – Area of OMACO
Therefore, required area = 
units
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2
The area bounded by the curve, x2 = 4y, and line, x = 4y – 2, is represented by the shaded area OBAO.
Let A and B be the points of intersection of the line and parabola.
Coordinates of point 
.
Coordinates of point B are (2, 1).
We draw AL and BM perpendicular to x-axis.
It can be observed that,
Area OBAO = Area OBCO + Area OACO … (1)
Then, Area OBCO = Area OMBC – Area OMBO
Similarly, Area OACO = Area OLAC – Area OLAO
Therefore, required area = 
Find the area of the region bounded by the curve y2 = 4x and the line x = 3
The region bounded by the parabola, y2 = 4x, and the line, x = 3, is the area OACO.
The area OACO is symmetrical about x-axis.
∴ Area of OACO = 2 (Area of OAB)
Therefore, the required area is 
units.
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. 
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.
Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is
A. 2
B. 
C. 
D. 
The area bounded by the curve, y2 = 4x, y-axis, and y = 3 is represented as
Thus, the correct answer is B.
How helpful was it?
How can we Improve it?
Please tell us how it changed your life *
Please enter your feedback
UrbanPro.com helps you to connect with the best Class 12 Tuition in India. Post Your Requirement today and get connected.
Find best tutors for Class 12 Tuition Classes by posting a requirement.
Get started now, by booking a Free Demo Class
