1. This document provides 31 multi-part questions involving calculating areas of regions bounded by curves using integration. The regions involve combinations of circles, parabolas, lines, and other curves. 2. The questions require setting up integral expressions to calculate the enclosed areas, evaluating the integrals, and obtaining numerical or algebraic answers for the region areas. 3. Integration is the primary technique used to solve these area calculation problems involving planar regions with curved boundaries.

1. CHAPTER – 8
APPLICATION OF INTEGRATION
6 Marks Questions:
1. Find the area of the region bounded by y2
= 9x , x = 2, x =4 and the x axis is in first quadrant.
[ 16 - 4 2 ]
2. Find the area bounded by curve x2
= 4y and the line x = 4y – 2.
3. Find the area of the region bounded by two parabolas y2
= x and x2
=y. [ 1/3]
4. Find the area of the region between parabola x2
= 4y and y2
= 4x . [ 16/3]
5. Find the area bounded by curves x2
+ y2
= 1 and (x – 1)2
+ y2
=1 .
2𝜋
3
−
3
2
6. Find the area of the region included between the curve 4y = 3x2
and line 2y = 3x + 12 . [27]
7. Using integration, find the area lying above x – axis and includes between x2
+ y2
= 8x and line
2y = 3x + 12. [27]
8. Find the area of that part of the circle x2
+ y2
= 16 which is exterior to parabola y2
= 6x.
9. Using integration, find the area between x2
+ y2
= 4 and (x – 2)2
+ y2
= 4.
8𝜋
3
+ 2 3 .
10. Using integration find the area of region bounded by the ∆ whose vertices are
(1,0) (2,2) and (3,1) . [3/2]
11. Find the area of region {(x,y) : x2
≤ 𝑦 ≤ 𝑥 } .
12. Find the area of region {(x,y) : y2
≤ 4𝑥 , 4𝑥2
+ 4𝑦2
≤ 9} .
13. Prove that the area between two parabolas y2
4ax and x2
= 4ay is 16 a2
/ 3 sq units.
14. Sketch the graph of y = 𝑥 + 3 and Evaluate 𝑥 + 3
0
−6
dx .
15. Find the area enclosed by the circle x2
+ y2
= 4 and line x + y = 2 .
16. Find the area of smaller region bounded by the ellipse
𝑥2
𝑎2 +
𝑦2
𝑏2 = 1 and line
𝑥
𝑎
+
𝑦
𝑏
= 1 .
17. Draw and sketch the following region and find its area {(x , y) : 𝑥2
+ 𝑦2
≤ 1 ≤ 𝑥 + 𝑦} .
18. Using integration , find the area of ∆ ABC where A (2,3), B (4,7), C (6,2).
19. Find the area bounded by curve y = cos x between x = 0 and x = 2𝜋 .
20. Find the area of the region : {(x,y) : 0 ≤ y ≤ 𝑥2
, 0 ≤ 𝑦 ≤ 𝑥 + 2, 0 ≤ 𝑥 ≤ 3} .[43/6]
21. Using the method of integration, find the area of the region bounded by the lines
2x+y = 4, 3x – 2y = 6, x – 3y +5 = 0. [7/2]
22. Find the area of the region included between y2
= x and line x + y = 2. [9/2]
23. Find the area between the curves y – x2
and y = x .

2. 24. Using the method of integration, find the area of the ∆ ABC, coordinate of whose vertices are A
(2,0), B (4,5), C (6,3). [7]
25. Find the area bounded by the circle x2
+ y2
= 16 and the line y = x in the first Quadrant.[2𝜋]
26. Using integration, find the area of the following region. 𝑥, 𝑦 :
𝑥2
9
+
𝑦2
4
≤ 1 ≤
𝑥
3
+
𝑦
2
.
27. Find the area of the region {(x, y) : x2
+ y2
≤ 4, 𝑥 + 𝑦 ≥ 2}.
28. Find the area lying above x – axis and included between the circle x2
+ y2
= 8x and the
parabola y2
= 4x.
29. Find the area of that part of the circle x2
+ y2
= 16 which is exterior to the parabola y2
= 6x.
30. Find the area of the region enclosed between the two circles x2
+ y2
= 9 and (x – 3)2
+ y2
= 9.
31. Using integration, find the area of the following region : {(x, y) : 𝑥 − 1 ≤ 𝑦 ≤ 5 − 𝑥2 } .
32. Using integration find the area of the triangular region whose sides have equations :
Y = 2x + 1, y = 3x + 1 and x = 4.