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## Chapter 5: Application of Definite Integration

### Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 5 Application of Definite Integration Exercise 5.1 [Page 187]

Find the area of the region bounded by the following curves, X-axis and the given lines: y = 2x, x = 0, x = 5

Find the area of the region bounded by the following curves, X-axis and the given lines: x = 2y, y = 0, y = 4

Find the area of the region bounded by the following curves, X-axis and the given lines : x = 0, x = 5, y = 0, y = 4

Find the area of the region bounded by the following curves, X-axis and the given lines : y = sin x, x = 0, x = `pi/(2)`

Find the area of the region bounded by the following curves, X-axis and the given lines: xy = 2, x = 1, x = 4

Find the area of the region bounded by the following curves, X-axis and the given lines : y^{2} = x, x = 0, x = 4

Find the area of the region bounded by the following curves, X-axis and the given lines: y^{2} = 16x, x = 0, x = 4

Find the area of the region bounded by the parabola: y^{2 }= 16x and its latus rectum.

Find the area of the region bounded by the parabola: y = 4 – x^{2} and the X-axis.

Find the area of the region included between: y^{2} = 2x and y = 2x

Find the area of the region included between: y^{2} = 4x, and y = x

Find the area of the region included between: y = x^{2} and the line y = 4x

Find the area of the region included between: y^{2} = 4ax and the line y = x

Find the area of the region included between: y = x^{2} + 3 and the line y = x + 3

### Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 5 Application of Definite Integration Miscellaneous Exercise 5 [Pages 188 - 190]

**Choose the correct option from the given alternatives :**

The area bounded by the regional ≤ x ≤ 5 and 2 ≤ y ≤ 5 is given by

12 sq units

8 sq units

25 sq units

32 sq units

**Choose the correct option from the given alternatives :**

The area of the region enclosed by the curve y = `(1)/x`, and the lines x = e, x = e^{2} is given by

1 sq unit

`(1)/(2) "sq unit"`

`(3)/(2) "sq units"`

`(5)/(2) "sq units"`

**Choose the correct option from the given alternatives :**

The area bounded by the curve y = x^{3}, the X-axis and the lines x = – 2 and x = 1 is

– 9 sq units

`-(15)/(4)"sq units"`

`(15)/(4)"sq units"`

`(17)/(4)"sq units"`

**Choose the correct option from the given alternatives :**

The area enclosed between the parabola y^{2} = 4x and line y = 2x is

`(2)/(3) "sq units"`

`(1)/(3) "sq unit"`

`(1)/(4) "sq unit"`

`(3)/(4) "sq unit"`

**Choose the correct option from the given alternatives :**

The area of the region bounded between the line x = 4 and the parabola y^{2} = 16x is

`(128)/(3)"sq units"`

`(108)/(3)"sq units"`

`(118)/(3)"sq units"`

`(218)/(3)"sq units"`

**Choose the correct option from the given alternatives :**

The area of the region bounded by y = cos x, Y-axis and the lines x = 0, x = 2π is

1 sq unit

2 sq units

3 sq units

4 sq units

**Choose the correct option from the given alternatives :**

The area bounded by the parabola y^{2} = 8x, the X-axis and the latus rectum is

`(31)/(3)"sq units"`

`(32)/(3)"sq units"`

`(32sqrt(2))/(3)"sq units"`

`(16)/(3)"sq units"`

**Choose the correct option from the given alternatives :**

The area under the curve y = `2sqrt(x)`, enclosed between the lines x = 0 and x = 1 is

4 sq units

`(3)/(4) "sq unit"`

`(2)/(3) "sq unit"`

`(4)/(3) "sq units"`

**Choose the correct option from the given alternatives :**

The area of the circle x^{2} + y^{2} = 25 in first quadrant is

`(25pi)/(4) "sq units"`

5π sq units

5 sq units

3 sq units

**Choose the correct option from the given alternatives :**

The area of the region bounded by the ellipse `x^2/a^2 + y^2/b^2` = 1 is

ab sq units

πab sq units

`pi/"ab" "sq units"`

πa

^{2}sq units

**Choose the correct option from the given alternatives :**

The area bounded by the parabola y^{2} = x and the line 2y = x is

`(4)/(3)"sq unit"`

1 sq unit

`(2)/(3)"sq unit"`

`(1)/(3)"sq unit"`

**Choose the correct option from the given alternatives :**

The area enclosed between the curve y = cos 3x, 0 ≤ x ≤ `pi/(6)` and the X-axis is

`(1)/(2)"sq unit"`

1 sq unit

`(2)/(3)"sq unit"`

`(1)/(3)"sq unit"`

**Choose the correct option from the given alternatives :**

The area bounded by y = `sqrt(x)` and the x = 2y + 3, X-axis in first quadrant is

`2sqrt(3) "sq units"`

9 sq units

`(34)/(3)"sq units"`

18 sq units

**Choose the correct option from the given alternatives :**

The area bounded by the ellipse `x^2/a^2 y^2/b^2` = 1 and the line `x/a + y/b` = 1 is

(πab – 2ab) sq units

`((piab)/4 - "ab"/2)"sq units"`

(πab – ab) sq units

πab sq units

**Choose the correct option from the given alternatives :**

The area bounded by the parabola y = x^{2} and the line y = x is

`(1)/(2)"sq unit"`

`(1)/(3)"sq unit"`

`(1)/(6)"sq unit"`

`(1)/(12)"sq unit"`

**Choose the correct option from the given alternatives :**

The area enclosed between the two parabolas y^{2} = 4x and y = x is

`(16)/(3)"sq units"`

`(32)/(3)"sq units"`

`(8)/(3)"sq units"`

`(4)/(3)"sq units"`

**Choose the correct option from the given alternatives :**

The area bounded by the curve y = tan x, X-axis and the line x = `pi/(4)` is

`(1)/(2) log 2 "sq units"`

log 2 sq units

2 log 2 sq units

3·log 2 sq units

**Choose the correct option from the given alternatives :**

The area of the region bounded by x^{2} = 16y, y = 1, y = 4 and x = 0 in the first quadrant, is

`(7)/(3)"sq units"`

`(8)/(3)"sq units"`

`(64)/(3)"sq units"`

`(56)/(3)"sq units"`

**Choose the correct option from the given alternatives :**

The area of the region included between the parabolas y^{2} = 4ax and x^{2} = 4ay, (a > 0) is given by

`(16a^2)/(3)"sq units"`

`(8a^2)/(3)"sq units"`

`(64)/(3)"sq units"`

`(56)/(3)"sq units"`

**Choose the correct option from the given alternatives :**

The area of the region included between the line x + y = 1 and the circle x^{2} + y^{2} = 1 is

`(pi/2 - 1)"sq units"`

(π – 2) sq units

`(pi/4 - 1/2)"sq units"`

`(pi - 1/2)"sq units"`

**Solve the following** :

Find the area of the region bounded by the following curve, the X-axis and the given lines : 0 ≤ x ≤ 5, 0 ≤ y ≤ 2

**Solve the following** :

Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = π

**Solve the following** :

Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = `pi/(3)`

**Solve the following : **

Find the area of the circle x^{2} + y^{2} = 9, using integration.

**Solve the following :**

Find the area of the ellipse `x^2/(25) + y^2/(16)` = 1 using integration

**Solve the following :**

Find the area of the region lying between the parabolas :

y^{2} = 4x and x^{2} = 4y

**Solve the following :**

Find the area of the region lying between the parabolas : 4y^{2} = 9x and 3x^{2} = 16y

**Solve the following :**

Find the area of the region lying between the parabolas : y^{2} = x and x^{2} = y.

**Solve the following :**

Find the area of the region in first quadrant bounded by the circle x^{2} + y^{2} = 4 and the X-axis and the line x = `ysqrt(3)`.

**Solve the following :**

Find the area of the region bounded by the parabola y^{2} = x and the line y = x in the first quadrant.

**Solve the following :**

Find the area enclosed between the circle x^{2} + y^{2} = 1 and the line x + y = 1, lying in the first quadrant.

**Solve the following :**

Find the area of the region bounded by the curve (y – 1)^{2} = 4(x + 1) and the line y = (x – 1).

**Solve the following :**

Find the area of the region bounded by the straight line 2y = 5x + 7, X-axis and x = 2, x = 5.

**Solve the following :**

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

## Chapter 5: Application of Definite Integration

## Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 5 - Application of Definite Integration

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 5 (Application of Definite Integration) 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 Maharashtra State Board Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 5 Application of Definite Integration are Application of Definite Integration, Area Bounded by the Curve, Axis and Line, Area Between Two Curves.

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