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

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Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board - Shaalaa.com
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Chapter 5: Application of Definite Integration

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 ≤ 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.

Chapter 5: Application of Definite Integration

Exercise 5.1Miscellaneous Exercise 5
Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board - Shaalaa.com

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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