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## Solutions for Chapter 5: Application of Definite Integration

Below listed, you can find solutions for Chapter 5 of Maharashtra State Board Balbharati for Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board.

### 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 1 ≤ 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.

## Solutions for 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

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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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