NCERT Solutions Class 12 Mathematics Chapter 8 Application Of Integrals Download In Pdf

Chapter 8 Application of Integrals Download in pdf

**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.
Fig

**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.** Find the area of the region bounded by the ellipse
2 2
1
16 9
x y + = .

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

**Question 6.** Find the area of the region in the first quadrant enclosed by x-axis, line x = 3 y
and the circle x2 + y2 = 4.

**Question **7. Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line
2
x= a .

**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.
Choose the correct answer in the following Exercises 12 and 13.

**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

(A) π

(B)
2
π

(C)
3
π

(D)
4
π

**Question 13. **Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is

(A) 2

(B)
9
4

(C)
9
3

(D)
9
2

EXERCISE 8.2

**Question 1.** Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y.

**Question 2.** Find the area bounded by curves (x – 1)2 + y2 = 1 and x2 + y2 = 1.

**Question 3.** Find the area of the region bounded by the curves y = x2 + 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).

**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.Choose the correct answer in the following exercises 6 and 7.

**Question 6.** 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)

**Question 7. **Area lying between the curves y2 = 4x and y = 2x is

(A)
2
3

(B)
1
3

(C)
1
4

(D)
3
4

Miscellaneous Exercise on Chapter 8

**Question 1.** 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

**Question 2. **Find the area between the curves y = x and y = x2.

**Question 3.** Find the area of the region lying in the first quadrant and bounded by y = 4x2,
x = 0, y = 1 and y = 4.

**Question 4. **Sketch the graph of y = x + 3 and evaluate 0
6
3
−
∫ x + dx .

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

**Question 6.** Find the area enclosed between the parabola y2 = 4ax and the line y = mx.

**Question 7.** Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12.

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

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

**Question 10. **Find the area of the region enclosed by the parabola x2 = 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 .
[Hint: The required region is bounded by lines x + y = 1, x– y = 1, – x + y = 1 and
– x – y = 1].

**Question 12.** Find the area bounded by curves {(x, y) : y ≥ x2 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) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}
Choose the correct answer in the following Exercises from 16 to 20.
16. Area bounded by the curve y = x3, the x-axis and the ordinates x = – 2 and x = 1 is

(A) – 9

(B)
15
4
−

(C)
15
4

(D)
17
4

**Question 17.** The area bounded by the curve y = x | x | , x-axis and the ordinates x = – 1 and
x = 1 is given by
(

A) 0

(B)
1
3

(C)
2
3

(D)
4
3

[Hint : y = x2 if x > 0 and y = – x2 if x < 0].

**Question 18.** The area of the circle x2 + y2 = 16 exterior to the parabola y2 = 6x is

(A)
4 (4 3)
3
π −

(B)
4 (4 3)
3
π +

(C)
4 (8 3)
3
π −

(D)
4 (8 3)
3
π +

**Question 19.** The area bounded by the y-axis, y = cos x and y = sin x when 0
2
x
π
≤ ≤ is

(A) 2 ( 2 −1)

(B) 2 −1

(C) 2 +1

(D) 2

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- Chapter 1 Relations and Functions
- Chapter 2 Inverse Trigonometric Functions
- Chapter 3 Matrices
- Chapter 4 Determinants
- Chapter 5 Continuity and Differentiability
- Chapter 6 Application of Derivatives
- Chapter 7 Integral
- Chapter 8 Application of Integrals
- Chapter 9 Differential Equations
- Chapter 10 Vector Algebra
- Chapter 11 Three Dimensional Geometry
- Chapter 12 Linear Programming
- Chapter 13 Probability

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