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

Mathematics Textbook for Class 12

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Chapters

NCERT Mathematics Class 12

Mathematics Textbook for Class 12

Chapter 8 : Application of Integrals

Pages 365 - 366

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.

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.

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.

Q 4 | Page 366

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

Q 5 | Page 366

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

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`

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.

Q 9 | Page 366

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

Q 10 | Page 366

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

Q 11 | Page 366

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

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`

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

Pages 371 - 372

Q 1 | Page 371

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

Q 2 | Page 371

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

Q 3 | Page 371

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

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).

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.

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)

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

Pages 375 - 376

Q 1.1 | Page 375

Find the area under the given curves and given lines:

y = x2x = 1, x = 2 and x-axis

Q 1.2 | Page 375

Find the area under the given curves and given lines:

y = x4x = 1, x = 5 and x –axis

Q 2 | Page 375

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

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

Q 4 | Page 375

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

Q 5 | Page 375

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

 
Q 6 | Page 375

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

Q 7 | Page 375

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

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`

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`

Q 10 | Page 375

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

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].

Q 12 | Page 376

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

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).

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

Q 15 | Page 376

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

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`

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`

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)`

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`

NCERT Mathematics Class 12

Mathematics Textbook for Class 12

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

NCERT solutions for Class 12 Maths chapter 8 (Application of Integrals) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Textbook for Class 12 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 12 Mathematics 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 solutions Application of Integrals exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 12 prefer NCERT Textbook Solutions to score more in exam.

Get the free view of chapter 8 Application of Integrals Class 12 extra questions for Maths and can use shaalaa.com to keep it handy for your exam preparation

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