NCERT solutions for Class 12 Maths chapter 8 - Application of Integrals [Latest edition]

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Solutions for Chapter 8: Application of Integrals

Below listed, you can find solutions for Chapter 8 of CBSE, Karnataka Board PUC NCERT for Class 12 Maths.


Exercise 8.1Exercise 8.2Exercise 8.3
Exercise 8.1 [Pages 365 - 366]

NCERT solutions for Class 12 Maths Chapter 8 Application of Integrals Exercise 8.1 [Pages 365 - 366]

Exercise 8.1 | Q 1 | Page 365

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

Exercise 8.1 | Q 2 | Page 365

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

Exercise 8.1 | Q 3 | Page 366

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

Exercise 8.1 | Q 4 | Page 366

Find the area of the region bounded by the ellipse  `x^2/16 + y^2/9 = 1`

Exercise 8.1 | Q 5 | Page 366

Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1`

Exercise 8.1 | Q 6 | Page 366

Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.

Exercise 8.1 | Q 7 | Page 366

Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line  `x = a/sqrt2`

Exercise 8.1 | Q 8 | Page 366

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

Exercise 8.1 | Q 9 | Page 366

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

Exercise 8.1 | Q 10 | Page 366

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

Exercise 8.1 | Q 11 | Page 366

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

Exercise 8.1 | Q 12 | Page 366

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

A. π

B. `pi/2`

C. `pi/3`

D. `pi/4`

Exercise 8.1 | Q 13 | Page 366

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

A. 2

B. 9/4

C. 9/3

D. 9/2

Exercise 8.2 [Pages 371 - 372]

NCERT solutions for Class 12 Maths Chapter 8 Application of Integrals Exercise 8.2 [Pages 371 - 372]

Exercise 8.2 | Q 1 | Page 371

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

Exercise 8.2 | Q 2 | Page 371

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

Exercise 8.2 | Q 3 | Page 371

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

Exercise 8.2 | Q 4 | Page 371

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

Exercise 8.2 | Q 5 | Page 371

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

Exercise 8.2 | Q 6 | Page 372

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)

Exercise 8.2 | Q 7 | Page 372

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

A. 2/3

B. 1/3

C. 1/4

D. 3/4

Exercise 8.3 [Pages 375 - 376]

NCERT solutions for Class 12 Maths Chapter 8 Application of Integrals Exercise 8.3 [Pages 375 - 376]

Exercise 8.3 | Q 1.1 | Page 375

Find the area under the given curves and given lines:

y = x2x = 1, x = 2 and x-axis

Exercise 8.3 | Q 1.2 | Page 375

Find the area under the given curves and given lines:

y = x4x = 1, x = 5 and x –axis

Exercise 8.3 | Q 2 | Page 375

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

Exercise 8.3 | Q 3 | Page 375

Find the area of the region lying in the first quadrant and bounded by y = 4x2x = 0, y = 1 and = 4

Exercise 8.3 | Q 4 | Page 375

Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`

Exercise 8.3 | Q 5 | Page 375

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

 
Exercise 8.3 | Q 6 | Page 375

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

Exercise 8.3 | Q 7 | Page 375

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

Exercise 8.3 | Q 8 | Page 375

Find the area of the smaller region bounded by the ellipse `x^2/9 + y^2/4` and the line `x/3 + y/2 = 1`

Exercise 8.3 | Q 9 | Page 375

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`

Exercise 8.3 | Q 10 | Page 375

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

Exercise 8.3 | Q 11 | Page 375

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].

Exercise 8.3 | Q 12 | Page 376

Find the area bounded by curves {(x, y) : y ≥ x2 and y = |x|}.

Exercise 8.3 | Q 13 | Page 376

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).

Exercise 8.3 | Q 14 | Page 376

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

Exercise 8.3 | Q 15 | Page 376

Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}

Exercise 8.3 | Q 16 | Page 376

Choose the correct answer 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`

Exercise 8.3 | Q 17 | Page 376

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

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

A. 0

B. `1/3`

C. `2/3`

D. `4/3`

Exercise 8.3 | Q 18 | Page 376

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

A. `4/3 (4pi - sqrt3)`

B. `4/3 (4pi + sqrt3)`

C. `4/3 (8pi - sqrt3)`

D.`4/3 (4pi + sqrt3)`

Exercise 8.3 | Q 19 | Page 376

The area bounded by the y-axis, y = cos x and y = sin x when  0 <= x <= `pi/2`

(A) 2 ( 2 −1)

(B) `sqrt2 -1`

(C) `sqrt2 + 1`

D. `sqrt2`

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Solutions for Chapter 8: Application of Integrals

Exercise 8.1Exercise 8.2Exercise 8.3

NCERT solutions for Class 12 Maths chapter 8 - Application of Integrals

Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Class 12 Maths CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Class 12 Maths CBSE, Karnataka Board PUC 8 (Application of Integrals) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in Class 12 Maths chapter 8 Application of Integrals are Area of the Region Bounded by a Curve and a Line, Area Between Two Curves, Area Under Simple Curves.

Using NCERT Class 12 Maths solutions Application of Integrals exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE, Karnataka Board PUC Class 12 Maths students prefer NCERT Textbook Solutions to score more in exams.

Get the free view of Chapter 8, Application of Integrals Class 12 Maths additional questions for Mathematics Class 12 Maths CBSE, Karnataka Board PUC, and you can use Shaalaa.com to keep it handy for your exam preparation.

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