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NCERT solutions Mathematics Class 12 Part 2 chapter 8 Application of Integrals

Chapters

NCERT Mathematics Class 12 Part 2

Mathematics Textbook for Class 12 Part 2

Chapter 8 - Application of Integrals

Pages 365 - 366

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

Q 1 | 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 2 | Page 365

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

Q 3 | Page 366

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

Q 4 | Page 366

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

Q 5 | 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 6 | Page 366

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

Q 7 | 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 8 | Page 366

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

Q 9 | Page 366

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

Q 10 | Page 366

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

Q 11 | 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 12 | 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

Q 13 | Page 366

Pages 371 - 372

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

Q 1 | Page 371

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

Q 2 | Page 371

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

Q 3 | 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 4 | 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 5 | Page 371

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 6 | 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

Q 7 | Page 372

Pages 375 - 376

Find the area under the given curves and given lines:

y = x2x = 1, x = 2 and x-axis

Q 1.1 | Page 375

Find the area under the given curves and given lines:

y = x4x = 1, x = 5 and x –axis

Q 1.2 | Page 375

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

Q 2 | Page 375

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

Q 3 | Page 375

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

Q 4 | Page 375

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

 
Q 5 | Page 375

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

Q 6 | Page 375

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

Q 7 | 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 8 | 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 9 | Page 375

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

Q 10 | 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 11 | Page 375

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

Q 12 | 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 13 | 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 14 | Page 376

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

Q 15 | 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 16 | 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 17 | 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 18 | 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`

Q 19 | Page 376

NCERT Mathematics Class 12 Part 2

Mathematics Textbook for Class 12 Part 2
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