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

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

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

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

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

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

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

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

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

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

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

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. `pi/2`

C. `pi/3`

D. `pi/4`

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

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

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

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

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

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)

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

A. 2/3

B. 1/3

C. 1/4

D. 3/4

Find the area under the given curves and given lines:

y = x², x = 1, x = 2 and x-axis

Find the area under the given curves and given lines:

y = x⁴, x = 1, x = 5 and x –axis

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

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

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

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`

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`

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].

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

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).

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

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

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`

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`

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)`

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`