![CHAPTER – 8 APPLICATION OF INTEGRALS
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. Find the area of that part of the circle x2
+ y2
= 16 which is exterior to parabola y2
= 6x.
8. Using integration, find the area between x2
+ y2
= 4 and (x – 2)2
+ y2
= 4.
9. Using integration find the area of region bounded by the ∆ whose vertices are (1,0) (2,2) and (3,1) . [3/2]
10. Find the area of region {(x,y) : x2
≤ 𝑦 ≤ 𝑥 } .
11. Find the area of region {(x,y) : y2
≤ 4𝑥 , 4𝑥2
+ 4𝑦2
≤ 9} .
12. Prove that the area between two parabolas y2
4ax and x2
= 4ay is 16 a2
/ 3 sq units.
13. Sketch the graph of y = 𝑥 + 3 and Evaluate 𝑥 + 3
0
−6
dx .
14. Find the area enclosed by the circle x2
+ y2
= 4 and line x + y = 2 .
15. Find the area of smaller region bounded by the ellipse
𝑥2
𝑎2 +
𝑦2
𝑏2 = 1 and line
𝑥
𝑎
+
𝑦
𝑏
= 1 .
16. Draw and sketch the following region and find its area {(x , y) : 𝑥2
+ 𝑦2
≤ 1 ≤ 𝑥 + 𝑦} .
17. Using integration , find the area of ∆ ABC where A (2,3), B (4,7), C (6,2).
18. 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]
19. Find the area of the region included between y2
= x and line x + y = 2. [9/2]
20. Find the area bounded by the circle x2
+ y2
= 16 and the line y = x in the first Quadrant. [2𝜋]
21. Using integration, find the area of the following region. 𝑥, 𝑦 :
𝑥2
9
+
𝑦2
4
≤ 1 ≤
𝑥
3
+
𝑦
2
.
22. Find the area of the region {(x, y) : x2
+ y2
≤ 4, 𝑥 + 𝑦 ≥ 2}.
23. Find the area of the region enclosed between the two circles x2
+ y2
= 9 and (x – 3)2
+ y2
= 9.
24. Using integration, find the area of the following region : {(x, y) : 𝑥 − 1 ≤ 𝑦 ≤ 5 − 𝑥2 } .
25. Using integration find the area of the triangular region whose sides have equations :
y = 2x + 1, y = 3x + 1 and x = 4.
26. The area between x= y2
and x=4 is divided into two equal parts by the line x=a, find a.
27. Find the smaller area between circle x2
+y2
=4 and the line x+y=2.
28. Using the method of integration find the area bounded by the curve |x| +|y|=1
29. Using integration, find the area of the triangle formed by positive x-axis and tangent and normal to the circle
x2
+y2
=4 at (1, 3)](https://image.slidesharecdn.com/applicationofintegrals-190814071321/85/Application-of-integrals-1-320.jpg)
Application of integrals
- 1. CHAPTER – 8 APPLICATION OF INTEGRALS 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. Find the area of that part of the circle x2 + y2 = 16 which is exterior to parabola y2 = 6x. 8. Using integration, find the area between x2 + y2 = 4 and (x – 2)2 + y2 = 4. 9. Using integration find the area of region bounded by the ∆ whose vertices are (1,0) (2,2) and (3,1) . [3/2] 10. Find the area of region {(x,y) : x2 ≤ 𝑦 ≤ 𝑥 } . 11. Find the area of region {(x,y) : y2 ≤ 4𝑥 , 4𝑥2 + 4𝑦2 ≤ 9} . 12. Prove that the area between two parabolas y2 4ax and x2 = 4ay is 16 a2 / 3 sq units. 13. Sketch the graph of y = 𝑥 + 3 and Evaluate 𝑥 + 3 0 −6 dx . 14. Find the area enclosed by the circle x2 + y2 = 4 and line x + y = 2 . 15. Find the area of smaller region bounded by the ellipse 𝑥2 𝑎2 + 𝑦2 𝑏2 = 1 and line 𝑥 𝑎 + 𝑦 𝑏 = 1 . 16. Draw and sketch the following region and find its area {(x , y) : 𝑥2 + 𝑦2 ≤ 1 ≤ 𝑥 + 𝑦} . 17. Using integration , find the area of ∆ ABC where A (2,3), B (4,7), C (6,2). 18. 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] 19. Find the area of the region included between y2 = x and line x + y = 2. [9/2] 20. Find the area bounded by the circle x2 + y2 = 16 and the line y = x in the first Quadrant. [2𝜋] 21. Using integration, find the area of the following region. 𝑥, 𝑦 : 𝑥2 9 + 𝑦2 4 ≤ 1 ≤ 𝑥 3 + 𝑦 2 . 22. Find the area of the region {(x, y) : x2 + y2 ≤ 4, 𝑥 + 𝑦 ≥ 2}. 23. Find the area of the region enclosed between the two circles x2 + y2 = 9 and (x – 3)2 + y2 = 9. 24. Using integration, find the area of the following region : {(x, y) : 𝑥 − 1 ≤ 𝑦 ≤ 5 − 𝑥2 } . 25. Using integration find the area of the triangular region whose sides have equations : y = 2x + 1, y = 3x + 1 and x = 4. 26. The area between x= y2 and x=4 is divided into two equal parts by the line x=a, find a. 27. Find the smaller area between circle x2 +y2 =4 and the line x+y=2. 28. Using the method of integration find the area bounded by the curve |x| +|y|=1 29. Using integration, find the area of the triangle formed by positive x-axis and tangent and normal to the circle x2 +y2 =4 at (1, 3)