#### Chapters

## Chapter 8 - Application of Integrals

#### Pages 365 - 366

Find the area of the region bounded by the curve *y*^{2} = *x* and the lines *x* = 1, *x* = 4 and the *x*-axis.

Find the area of the region bounded by *y*^{2} = 9*x*,* x* = 2, *x* = 4 and the *x*-axis in the first quadrant.

Find the area of the region bounded by *x*^{2} = 4*y*, *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 x^{2} + y^{2} = 4.

Find the area of the smaller part of the circle *x*^{2} +* y*^{2} = *a*^{2} cut off by the line `x = a/sqrt2`

The area between *x* = *y*^{2} 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 *x*^{2} = 4*y* and the line *x* = 4*y *– 2

Find the area of the region bounded by the curve *y*^{2} = 4*x* and the line *x* = 3

Area lying in the first quadrant and bounded by the circle *x*^{2} + *y*^{2} = 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 *y*^{2} = 4*x*, *y*-axis and the line *y* = 3 is

**A.** 2

**B.** 9/4

**C.** 9/3

**D. 9/2**

#### Pages 371 - 372

Find the area of the circle 4*x*^{2} + 4*y*^{2} = 9 which is interior to the parabola *x*^{2} = 4*y*

Find the area bounded by curves (*x* – 1)^{2} + *y*^{2} = 1 and *x*^{2} + *y*^{ 2} = 1

Find the area of the region bounded by the curves *y* = *x*^{2 }+ 2, *y *= *x*, *x* = 0 and *x* = 3

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* = 2*x* +1, *y* = 3*x* + 1 and *x *= 4.

Smaller area enclosed by the circle *x*^{2} + *y*^{2} = 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 *y*^{2} = 4*x* and *y* = 2*x* is

**A.** 2/3

**B.** 1/3

**C.** 1/4

**D. 3/4**

#### Pages 375 - 376

Find the area under the given curves and given lines:

*y* = *x*^{2}, *x* = 1, *x* = 2 and *x*-axis

Find the area under the given curves and given lines:

*y* = *x*^{4}, *x* = 1, *x* = 5 and *x* –axis

Find the area between the curves *y* = *x* and *y* = *x*^{2}

Find the area of the region lying in the first quadrant and bounded by *y* = 4*x*^{2}, *x* = 0, *y* = 1 and *y *= 4

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

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

Find the area enclosed between the parabola *y*^{2} = 4*ax* and the line* y *= *mx*

Find the area enclosed by the parabola 4*y* = 3*x*^{2} and the line 2*y* = 3*x* + 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`

Find the area of the region enclosed by the parabola *x*^{2} = *y*, the line *y* = *x* + 2 and *x*-axis

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: 2*x* + *y* = 4, 3*x* – 2*y* = 6 and *x* – 3*y *+ 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* = *x*^{3}, 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* = *x*^{2} if *x* > 0 and *y* = –*x*^{2} if *x* < 0]

**A.** 0

**B.** `1/3`

**C.** `2/3`

**D. `4/3`**

Choose the correct answer The area of the circle *x*^{2} + *y*^{2} = 16 exterior to the parabola *y*^{2} = 6*x* 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`

#### Textbook solutions 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 Part 2 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