# NCERT Solutions for Class 12 Maths Maths Part-2 Chapter 8

## Application of Integrals Class 12

### Exercise 8.1 : Solutions of Questions on Page Number : 365

Q1 :

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

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

Q2 :

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

The area of the region bounded by the curve, y2 = 9x, x = 2, and x = 4, and the x-axis is the area ABCD.

Q3 :

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

Q4 :

Find the area of the region bounded by the ellipse

Q5 :

Find the area of the region bounded by the ellipse

Q6 :

Find the area of the region in the first quadrant enclosed by x-axis, line and the circle

Q7 :

Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line

Q8 :

The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.

Q9 :

Find the area of the region bounded by the parabola y = x2 and

Q10 :

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

Q11 :

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

Q12 :

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

A. π

B.

C.

D.

Q13 :

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

A. 2

B.

C.

D.

### Exercise 8.2 : Solutions of Questions on Page Number : 371

Q1 :

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

Q2 :

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

Q3 :

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

Q4 :

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

Q5 :

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

A. 2 (π - 2)

B. π - 2

C. 2π - 1

D. 2 (π + 2)

Q6 :

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

A.

B.

C.

D.

### Exercise Miscellaneous : Solutions of Questions on Page Number : 375

Q1 :

Find the area under the given curves and given lines:

(i) y = x2, x = 1, x = 2 and x-axis

(ii) y = x4, x = 1, x = 5 and x -axis

Q2 :

Find the area between the curves y = x and y = x2

Q3 :

Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0, y = 1 and y = 4

Q4 :

Sketch the graph of and evaluate

Q5 :

Find the area bounded by the curve y = sin x between x = 0 and x = 2π

Q6 :

Find the area enclosed between the parabola y2 = 4ax and the line y = mx

Q7 :

Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12

Q8 :

Find the area of the smaller region bounded by the ellipse and the line

Q9 :

Find the area of the smaller region bounded by the ellipse and the line

Q10 :

Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis

Q11 :

Using the method of integration find the area bounded by the curve

[Hint: the required region is bounded by lines x + y = 1, x â€“ y = 1, â€“ x + y = 1 and â€“ x â€“ y = 11]

Q12 :

Find the area bounded by curves

Q13 :

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

Q14 :

Find the area of the region

Q15 :

Area bounded by the curve y = x3, the x-axis and the ordinates x = â€“2 and x = 1 is

A. â€“ 9

B.

C.

D.

Q16 :

The area bounded by the curve, x-axis and the ordinates x = â€“1 and x = 1 is given by

[Hint: y = x2 if x > 0 and y = â€“x2 if x < 0]

A. 0

B.

C.

D.

Q17 :

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

A.

B.

C.

D.

Q18 :

The area bounded by the y-axis, y = cos x and y = sin x when

A.

B.

C.

D.