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

#### Chapters ## 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.

Exercise 5.1Miscellaneous Exercise 5
Exercise 5.1 [Page 187]

### 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]

Exercise 5.1 | Q 1.1 | 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

Exercise 5.1 | Q 1.2 | Page 187

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

Exercise 5.1 | Q 1.3 | Page 187

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

Exercise 5.1 | Q 1.4 | Page 187

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)

Exercise 5.1 | Q 1.5 | Page 187

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

Exercise 5.1 | Q 1.6 | Page 187

Find the area of the region bounded by the following curves, X-axis and the given lines : y2 = x, x = 0, x = 4

Exercise 5.1 | Q 1.7 | Page 187

Find the area of the region bounded by the following curves, X-axis and the given lines: y2 = 16x, x = 0, x = 4

Exercise 5.1 | Q 2.1 | Page 187

Find the area of the region bounded by the parabola: y2 = 16x and its latus rectum.

Exercise 5.1 | Q 2.2 | Page 187

Find the area of the region bounded by the parabola: y = 4 – x2 and the X-axis.

Exercise 5.1 | Q 3.1 | Page 187

Find the area of the region included between: y2 = 2x and y = 2x

Exercise 5.1 | Q 3.2 | Page 187

Find the area of the region included between: y2 = 4x, and y = x

Exercise 5.1 | Q 3.3 | Page 187

Find the area of the region included between: y = x2 and the line y = 4x

Exercise 5.1 | Q 3.4 | Page 187

Find the area of the region included between: y2 = 4ax and the line y = x

Exercise 5.1 | Q 3.5 | Page 187

Find the area of the region included between: y = x2 + 3 and the line y = x + 3

Miscellaneous Exercise 5 [Pages 188 - 190]

### 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]

Miscellaneous Exercise 5 | Q 1.01 | Page 188

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

Miscellaneous Exercise 5 | Q 1.02 | Page 188

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 = e2 is given by

• 1 sq unit

• (1)/(2) "sq unit"

• (3)/(2) "sq units"

• (5)/(2) "sq units"

Miscellaneous Exercise 5 | Q 1.03 | Page 188

Choose the correct option from the given alternatives :

The area bounded by the curve y = x3, 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"

Miscellaneous Exercise 5 | Q 1.04 | Page 188

Choose the correct option from the given alternatives :

The area enclosed between the parabola y2 = 4x and line y = 2x is

• (2)/(3) "sq units"

• (1)/(3) "sq unit"

• (1)/(4) "sq unit"

• (3)/(4) "sq unit"

Miscellaneous Exercise 5 | Q 1.05 | Page 188

Choose the correct option from the given alternatives :

The area of the region bounded between the line x = 4 and the parabola y2 = 16x is ______.

• (128)/(3)sq.units

• (108)/(3)sq.units

• (118)/(3)sq.units

• (218)/(3)sq.units

Miscellaneous Exercise 5 | Q 1.06 | Page 189

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

Miscellaneous Exercise 5 | Q 1.07 | Page 189

Choose the correct option from the given alternatives :

The area bounded by the parabola y2 = 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"

Miscellaneous Exercise 5 | Q 1.08 | Page 189

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"

Miscellaneous Exercise 5 | Q 1.09 | Page 189

Choose the correct option from the given alternatives :

The area of the circle x2 + y2 = 25 in first quadrant is

• (25pi)/(4) "sq units"

• 5π sq units

• 5 sq units

• 3 sq units

Miscellaneous Exercise 5 | Q 1.1 | Page 189

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"

• πa2 sq units

Miscellaneous Exercise 5 | Q 1.11 | Page 189

Choose the correct option from the given alternatives :

The area bounded by the parabola y2 = x and the line 2y = x is

• (4)/(3)"sq unit"

• 1 sq unit

• (2)/(3)"sq unit"

• (1)/(3)"sq unit"

Miscellaneous Exercise 5 | Q 1.12 | Page 189

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"

Miscellaneous Exercise 5 | Q 1.13 | Page 189

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

Miscellaneous Exercise 5 | Q 1.14 | Page 189

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

Miscellaneous Exercise 5 | Q 1.15 | Page 189

Choose the correct option from the given alternatives :

The area bounded by the parabola y = x2 and the line y = x is

• (1)/(2)"sq unit"

• (1)/(3)"sq unit"

• (1)/(6)"sq unit"

• (1)/(12)"sq unit"

Miscellaneous Exercise 5 | Q 1.16 | Page 189

Choose the correct option from the given alternatives :

The area enclosed between the two parabolas y2 = 4x and y = x is

• (16)/(3)"sq units"

• (32)/(3)"sq units"

• (8)/(3)"sq units"

• (4)/(3)"sq units"

Miscellaneous Exercise 5 | Q 1.17 | Page 190

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

Miscellaneous Exercise 5 | Q 1.18 | Page 190

Choose the correct option from the given alternatives :

The area of the region bounded by x2 = 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"

Miscellaneous Exercise 5 | Q 1.19 | Page 190

Choose the correct option from the given alternatives :

The area of the region included between the parabolas y2 = 4ax and x2 = 4ay, (a > 0) is given by

• (16a^2)/(3)"sq units"

• (8a^2)/(3)"sq units"

• (64)/(3)"sq units"

• (56)/(3)"sq units"

Miscellaneous Exercise 5 | Q 1.2 | Page 190

Choose the correct option from the given alternatives :

The area of the region included between the line x + y = 1 and the circle x2 + y2 = 1 is

• (pi/2 - 1)"sq units"

• (π – 2) sq units

• (pi/4 - 1/2)"sq units"

• (pi - 1/2)"sq units"

Miscellaneous Exercise 5 | Q 2.01 | Page 190

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

Miscellaneous Exercise 5 | Q 2.01 | Page 190

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

Miscellaneous Exercise 5 | Q 2.01 | Page 190

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)

Miscellaneous Exercise 5 | Q 2.02 | Page 190

Solve the following :

Find the area of the circle x2 + y2 = 9, using integration.

Miscellaneous Exercise 5 | Q 2.03 | Page 190

Solve the following :

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

Miscellaneous Exercise 5 | Q 2.04 | Page 190

Solve the following :

Find the area of the region lying between the parabolas :
y2 = 4x and x2 = 4y

Miscellaneous Exercise 5 | Q 2.04 | Page 190

Solve the following :

Find the area of the region lying between the parabolas : 4y2 = 9x and 3x2 = 16y

Miscellaneous Exercise 5 | Q 2.04 | Page 190

Solve the following :

Find the area of the region lying between the parabolas : y2 = x and x2 = y.

Miscellaneous Exercise 5 | Q 2.05 | Page 190

Solve the following :

Find the area of the region in first quadrant bounded by the circle x2 + y2 = 4 and the X-axis and the line x = ysqrt(3).

Miscellaneous Exercise 5 | Q 2.06 | Page 190

Solve the following :

Find the area of the region bounded by the parabola y2 = x and the line y = x in the first quadrant.

Miscellaneous Exercise 5 | Q 2.07 | Page 190

Solve the following :

Find the area enclosed between the circle x2 + y2 = 1 and the line x + y = 1, lying in the first quadrant.

Miscellaneous Exercise 5 | Q 2.08 | Page 190

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).

Miscellaneous Exercise 5 | Q 2.09 | Page 190

Solve the following :

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

Miscellaneous Exercise 5 | Q 2.1 | Page 190

Solve the following :

Find the area of the region bounded by the curve y = 4x2, Y-axis and the lines y = 1, y = 4.

## Solutions for Chapter 5: Application of Definite Integration

Exercise 5.1Miscellaneous Exercise 5 ## 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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