NCERT Solutions for Class 12 Mathemetics Chapter 8 - Applications of the Integrals

Question 1:

Find the area of the region bounded by the curve y² = x and the lines x = 1, x = 4 and the x-axis.

Question 2:

Find the area of the region bounded by y² = 9x, x = 2, x = 4 and the x-axis in the first quadrant.

Question 3:

Find the area of the region bounded by x² = 4y, y = 2, y = 4 and the y-axis in the first quadrant.

Question 4:

Question 5:

Question 6:

Question 7:

Question 8:

The area between x = y² 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 = x² and y = | x |.

Question 10:

Find the area bounded by the curve x² = 4y and the line x = 4y – 2.

Question 11:

Find the area of the region bounded by the curve y² = 4x and the line x = 3.

Question 12:

Area lying in the first quadrant and bounded by the circle x² + y² = 4 and the lines x = 0 and x = 2 is :

1. $\mathrm{\pi }$

2. 

3. 

4. 

Question 13:

Area of the region bounded by the curve y² = 4x, y-axis and the line y = 3 is :

1. 2

2. 

3. 

4. 

Question 14:

Find the area of the circle 4x² + 4y² = 9, which is interior to the parabola x² = 4y.

Question 15:

Find the area bounded by curves :

Question 16:

Find the area bounded by the curves :
y = x² + 2, y = x, x = 0 and x = 3.

Question 17:

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

Question 18:

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

Question 19:

Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is :

1. 2 ($\mathrm{\pi }$ – 2)
2. $\mathrm{\pi }$ – 2
3. 2$\mathrm{\pi }$ – 1
4. 2 ($\mathrm{\pi }$ + 2)

Question 20:

Area lying between the curves y² = 4x and y = 2x is :

Question 21:

Area lying in the first quadrant and bounded by the circle x² + y² = 4 and the lines x = 0 and x = 2 is :

1. $\mathrm{\pi }$

2. 

3. 

4. 

Question 22:

Area of the region bounded by the curve y² = 4x, y-axis and the line y = 3 is :

1. 2

2. 

3. 

4. 

Question 23:

Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is :

1. 2 ($\mathrm{\pi }$ – 2)
2. $\mathrm{\pi }$ – 2
3. 2 $\mathrm{\pi }$ – 1
4. 2 ($\mathrm{\pi }$ + 2)

Question 24:

Area lying between the curves y² = 4x and y = 2 is :

Question 25:

Area bounded by the curve y = x³, the x-axis and the ordinates x = – 2 and x = 1 is :

1. – 9

2. 

3. 

4. 

Question 26:

The area bounded by the curve y = x | x |, x-axis and the ordinates x = – 1 and x = 1 is given by :

1. 0

2. 

3. 

4. 

Question 27:

The area of the circle x² + y² = 16 exterior to the parabola y² = 6x is :

Question 28:

The area enclosed by the circle x² + y² = 2 is equal to :

1. 4$\mathrm{\pi }$ sq. units

2. 

3. 4$\mathrm{\pi }$² sq. units
4. 2$\mathrm{\pi }$ sq. units.

Question 29:

The area enclosed by the circle x² + y² = 2 is equal to :

1. 4$\mathrm{\pi }$ sq. units

2. 

3. 4$\mathrm{\pi }$² sq. units
4. 2$\mathrm{\pi }$ sq. units.

Question 30:

1. $\mathrm{\pi }$²ab
2. $\mathrm{\pi }$ ab
3. $\mathrm{\pi }$a²b
4. $\mathrm{\pi }$ab²

Question 31:

The area of the region bounded by the curve y = x² and the line y = 16 is :

Question 32:

Question 33:

The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is :