Maharashtra State BoardHSC Commerce 12th Board Exam
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Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 7 - Applications of Definite Integration [Latest edition]

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Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board - Shaalaa.com

Chapter 7: Applications of Definite Integration

Exercise 7.1Miscellaneous Exercise 7
Exercise 7.1 [Page 157]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 7 Applications of Definite Integration Exercise 7.1 [Page 157]

Exercise 7.1 | Q 1.1 | Page 157

Find the area of the region bounded by the following curves, the X-axis and the given lines:  y = x4, x = 1, x = 5

Exercise 7.1 | Q 1.2 | Page 157

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = `sqrt(6x + 4), x = 0, x = 2`

Exercise 7.1 | Q 1.3 | Page 157

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

Exercise 7.1 | Q 1.4 | Page 157

Find the area of the region bounded by the following curves, the X-axis and the given lines:  2y = 5x + 7, x = 2, x = 8

Exercise 7.1 | Q 1.5 | Page 157

Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4

Exercise 7.1 | Q 1.6 | Page 157

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x2 + 1, x = 0, x = 3

Exercise 7.1 | Q 1.7 | Page 157

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = 2 – x2, x = – 1, x = 1

Exercise 7.1 | Q 2 | Page 157

Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.

Exercise 7.1 | Q 3 | Page 157

Find the area of circle x2 + y2 = 25.

Exercise 7.1 | Q 4 | Page 157

Find the area of ellipse `x^2/(4) + y^2/(25)` = 1.

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Miscellaneous Exercise 7 [Pages 157 - 158]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 7 Applications of Definite Integration Miscellaneous Exercise 7 [Pages 157 - 158]

Miscellaneous Exercise 7 | Q 1.1 | Page 157

Choose the correct alternative :

Area of the region bounded by the curve x2 = y, the X-axis and the lines x = 1 and x = 3 is _______.

  • `(26)/(3)"sq. units"`

  • `(3)/(26)"sq. units"`

  • 26 sq. units

  • 3 sq. units

Miscellaneous Exercise 7 | Q 1.2 | Page 157

Choose the correct alternative :

The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.

  • 28 sq. units

  • 3 sq. units

  • `(56)/(3)"sq. units"`

  • `(63)/(7)"sq. units"`

Miscellaneous Exercise 7 | Q 1.3 | Page 157

Choose the correct alternative :

Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.

  • 53 sq. units

  • `(3)/(56)"sq. units"`

  • `(56)/(3)"sq. units"`

  • `(63)/(7)"sq. units"`

Miscellaneous Exercise 7 | Q 1.4 | Page 157

Choose the correct alternative :

Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _____.

  • `(3142)/(5)"sq.unts"`

  • `(3124)/(5)"sq.unts"`

  • `(3142)/(3)"sq.unts"`

  • `(3124)/(3)"sq.unts"`

Miscellaneous Exercise 7 | Q 1.5 | Page 157

Choose the correct alternative :

Using definite integration, area of circle x2 + y2 = 25 is _______.

  • 5π sq. units

  • 4π sq. units

  • 25π sq. units

  • 25 sq. units

Miscellaneous Exercise 7 | Q 2.1 | Page 158

Fill in the blank : 

Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.

Miscellaneous Exercise 7 | Q 2.2 | Page 158

Using definite integration, area of the circle x2 + y2 = 49 is _______.

Miscellaneous Exercise 7 | Q 2.3 | Page 158

Fill in the blank :

Area of the region bounded by x2 = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.

Miscellaneous Exercise 7 | Q 2.4 | Page 158

Fill in the blank :

The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 is _______.

Miscellaneous Exercise 7 | Q 2.5 | Page 158

Fill in the blank :

The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.

Miscellaneous Exercise 7 | Q 3.1 | Page 158

State whether the following is True or False :

The area bounded by the curve x = g (y), Y-axis and bounded between the lines y = c and y = d is given by `int_"c"^"d"x*dy = int_(y = "c")^(y = "d") "g"(y)*dy` 

  • True

  • False

Miscellaneous Exercise 7 | Q 3.2 | Page 158

State whether the following is True or False :

The area bounded by the two cures y = f(x), y = g (x) and X-axis is `|int_"a"^"b" f(x)*dx - int_"b"^"a" "g"(x)*dx|`.

  • True

  • False

Miscellaneous Exercise 7 | Q 3.3 | Page 158

State whether the following is True or False :

The area bounded by the curve y = f(x), X-axis and lines x = a and x = b is `|int_"a"^"b" f(x)*dx|`.

  • True

  • False

Miscellaneous Exercise 7 | Q 3.4 | Page 158

State whether the following is True or False :

If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b is positive.

  • True

  • False

Miscellaneous Exercise 7 | Q 3.5 | Page 158

State whether the following is True or False :

The area of the portion lying above the X-axis is positive.

  • True

  • False

Miscellaneous Exercise 7 | Q 4.1 | Page 158

Solve the following :

Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c.

Miscellaneous Exercise 7 | Q 4.2 | Page 158

Solve the following :

Find the area between the parabolas y2 = 7x and x2 = 7y.

Miscellaneous Exercise 7 | Q 4.3 | Page 158

Solve the following :

Find the area of the region bounded by the curve y = x2 and the line y = 10.

Miscellaneous Exercise 7 | Q 4.4 | Page 158

Solve the following :

Find the area of the ellipse `x^2/(16) + y^2/(9)` = 1.

Miscellaneous Exercise 7 | Q 4.5 | Page 158

Solve the following :

Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.

Miscellaneous Exercise 7 | Q 4.6 | Page 158

Solve the following :

Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.

Miscellaneous Exercise 7 | Q 4.7 | Page 158

Solve the following :

Find the area of the region bounded by the parabola y2 = 25x and the line x = 5.

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Chapter 7: Applications of Definite Integration

Exercise 7.1Miscellaneous Exercise 7
Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board - Shaalaa.com

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 7 - Applications of Definite Integration

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 7 (Applications 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 1 (Commerce) 12th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 7 Applications of Definite Integration are Standard Forms of Parabola and Their Shapes, Standard Forms of Ellipse, Area Under Simple Curves.

Using Balbharati 12th Board Exam solutions Applications of Definite Integration 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 Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 12th Board Exam prefer Balbharati Textbook Solutions to score more in exam.

Get the free view of chapter 7 Applications of Definite Integration 12th Board Exam extra questions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board and can use Shaalaa.com to keep it handy for your exam preparation

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