**Question 1. Find the area of the region bounded by the curve y ^{2} = x and the lines x = 1, x = 4, and the x-axis.**

**Question 2. Find the area of the region bounded by y ^{2} = 9x, x = 2, x = 4 and x-axis in the first quadrant.**

**Question 3. Find the area of the region bounded by x ^{2} = 4y, y = 2, y = 4 and the y-axis in the first quadrant.**

**Question 4. Find the area of the region bounded by the ellipse x ^{2}/16+y^{2}/9 = 1**

**Note:** If a curve makes same area in all 4 quadrants or in 2 quadrants (as in above question). Then we calculate the area in one quadrant and multiply it with 4, if the area is same in 4 quadrants or multiply it with 2, if the area is same in 2 quadrants.

**Question 5. Find the area of the region bounded by the ellipse x ^{2}/4+y^{2}/9 = 1**

**Question 6. Find the area of the region in the first quadrant enclosed by x-axis, line**

**Question 7. Find the area of the smaller part of the circle x ^{2} + y^{2} = a^{2} cut off by the line x= a/root2.**

**Question 8. The area between x = y ^{2} and x = 4 is divided into two equal parts by the line x = a, find the value of a.**

**Question 9. Find the area of the region bounded by the parabola y = x ^{2} and y = |x|**

**Question 10. Find the area bounded by the curve x ^{2} = 4y and the line x = 4y – 2**

**Question 11. Find the area of the region bounded by the curve y ^{2} = 4x and the line x = 3**

**Note: **Areas below and above x–axis are equal for a parabola or ellipse or hyperbola have the x-axis as its axis.

**Choose the correct answer in the following Questions 12 and 13 :**

#### Exercise 8.2

**Question 1. Find the area of the circle 4x ^{2} + 4y^{2} = 9 which is interior to the parabola x^{2} = 4y**

**Note: **In case of area between the two curves, we first calculate the points of intersection of the given curves and then integrate with proper limits

**Question 2. Find the area bounded by curves (x – 1) ^{2} + y^{2} = 1 and x^{2} + y^{2} = 1.**

**Sol.** Given circles are x^{2} + y^{2} = 1

and (x – 1)^{2} + y^{2} = 1 …..(ii)

Centre of …..(i) is O (0, 0) and radius =1

Centre of (ii) is (1, 0) and radius = 1

Both these circle are symmetrical about x-axis

**Question 3. Find the area of the region bounded by the curves y = x ^{2} + 2, y = x, x = 0 and x = 3.**

**Question 4. Using integration find the area of region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2).**

**Note: **If the three vertices of a triangle is given, the area is calculated by first finding the equations of three lines joining these three points and then integrate with proper limits

**Question 5. Using integration find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4**

**Question 6. Smaller area bounded by the circle x ^{2} + y^{2} = 4 and the line x + y =2**

**Question 7. Area lying between the curves y ^{2} = 4x and y = 2x.(a) 2/3 (b) 1/3(c) 1/4(d) 3/4**

#### Miscellaneous Exercise

**Question 1. Find the area under the given curves and given lines: (i) y = x ^{2}, x = 1, x = 2 and x-axis (ii) y = x^{4}, x = 1, x = 5 and x-axis**

**Question 2. Find the area between the curves y = x and y = x ^{2}.**

**Question 3. Find the area of the region lying in the first quadrant and bounded by y = 4x ^{2}, x = 0, y = 1 and y = 4.**

**Question 4. Sketch the graph of y = |x + 3| and evaluate**

**Question 5. Find the area bounded by the curve y = sin x between x = 0 and x = 2pi.**

**Question 6. Find the area enclosed between the parabola y ^{2} = 4ax and the line y = mx**

**Question 7. Find the area enclosed by the parabola 4y = 3x ^{2} and the line 2y = 3x + 12.**

**Question 8. Find the area of the smaller region bounded by the ellipse x ^{2}/9 + y^{2}/4 = 1 and the line x/3+ y/2 = 1.**

**Question 9. Find the area of the smaller region bounded by the ellipse x ^{2}/a^{2} + y^{2}/b^{2} = 1 and the line x/a+ y/b = 1**

**Question 10. Find the area of the region enclosed by the parabola x ^{2} = y, the line y = x + 2, and the x-axis**

**Question 11. Using the method of integration find the area bounded by the curve |x| + |y| = 1.**

**Question 12. Find the area bounded by curves [(x, y) : y ³ x ^{2} and y = |x|}.**

**Question 13. Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5) and C (6, 3)**

**Question 14. Using the method of integration find the area of the region bounded by lines: 2x + y = 4, 3x – 2y = 6 and x – 3y + 5 = 0**

**Question 15. Find the area of the region {(x, y) : y ^{2} <= 4x, 4x^{2} + 4y^{2} <= 9}**

**Choose the correct answer in the following questions from 16 to 19**

**Related Articles:**

- NCERT Solutions for Class 12 (All Subjects)
- NCERT Solutions for Class 12 Maths (Chapter-wise PDF)
- Application of Integrals Class 12 Notes Mathematics Chapter 8