Table of Contents
Chapter 21 Areas of bounded regions Exercise Ex. 21.1
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Thus, Required area = square unitsQuestion 8
Solution 8
Question 9
Solution 9
Question 11
Sketch the region {(x, y):9x2 + 4y2 = 36} and find the area enclosed by it, using integration.Solution 11
9x2 + 4y2 = 36
Area of Sector OABCO =
Area of the whole figure = 4 × Ar. D OABCO
= 6p sq. unitsQuestion 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
What dose this integral represent on the graph?.Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
Solution 26
Question 10
and evaluate the area of the region under the curve and above the x-axis.Solution 10
Question 27
Find the area of the minor segment of the circle x2 + y2 = a2 cut off by the line x =Solution 27
Question 28
Find the area of the region bounded by the curve x = at2, y = 2at between the ordinates corresponding t = 1 and t = 2.Solution 28
Question 29
Find the area enclosed by the curve x = 3 cost,
y = 2 sin t.Solution 29
Chapter 21 Areas of Bounded Regions Exercise Ex. 21.2
Question 1
Solution 1
Question 2
Solution 2
Question 3
Find the area of the region bounded by x2 = 4ay and its latusrectum.Solution 3
Question 4
Find the area of the region bounded by x2 + 16y = 0 and its latusrectum.Solution 4
Question 5
Find the area of the region bounded by the curve ay2 = x3, the y-axis and the lines y = a and y = 2a.Solution 5
Chapter 21 – Areas of Bounded Regions Exercise Ex. 21.3
Question 2
Find the area of the region common to the parabolas 4y2 = 9x and 3x2 = 16y.Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Find the area of the region between the circles x2 + y2 = 4 and (x – 2)2 + y2 = 4.Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23 (i)
Using Integration, find the area of the region bounded by the triangle whose vertices are (- 1, 2), (1, 5) and (3, 4).Solution 23 (i)
Equation of side AB,
Equation of side BC,
Equation of side AC,
Area of required region
= Area of EABFE + Area of BFGCB – Area of AEGCA
Question 25
Solution 25
Question 26
Solution 26
Question 27
Solution 27
Question 29
Solution 29
Question 31
Solution 31
Question 32
Solution 32
Question 33
Solution 33
Question 34
Solution 34
Question 35
Solution 35
Question 36
Solution 36
Question 37
Solution 37
Question 39
Solution 39
Question 40
Solution 40
Question 41
Solution 41
Question 42
Solution 42
Question 43
Solution 43
Question 44
Solution 44
Question 46
Solution 46
Question 47
Solution 47
Question 48
Solution 48
Question 49
Solution 49
Question 50
Solution 50
Question 1
Calculate the area of the region bounded by the parabolas y2 = 6x and x2 = 6y.Solution 1
Question 18
Find the area of the region bounded by y =, x = 2y + 3 in the first quadrant and x-axis.Solution 18
Question 24
Find the area of the bounded by y =and y = x.Solution 24
Question 28
Find the area enclosed by the curve y = -x2 and the straight line x + y + 2 = 0.Solution 28
Question 30
Using the method of integration, find the area of the region bounded by the following lines: 3x – y – 3 = 0,
2x + y – 12 = 0, x – 2y – 1 = 0.Solution 30
Question 38
Find the area of the region enclosed by the parabola
x2 = y and the line y = x + 2.Solution 38
Question 51
Solution 51
Question 52
Solution 52
Chapter 21 Areas of Bounded Regions Exercise Ex. 21.4
Question 1
Find the area of the region between the parabola x = 4y – y2 and the line x = 2y – 3.Solution 1
Question 2
Find the area bounded by the parabola x = 8 + 2y – y2; the y-axis and the lines y = -1 and y = 3.Solution 2
Question 3
Find the area bounded by the parabola y2 = 4x and the line
y = 2x – 4.
i. By using horizontal strips
ii. By using vertical stripsSolution 3
Question 4
Find the area of the region bounded the parabola y2 = 2x and straight line x – y = 4.Solution 4
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