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## 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 Exercise 7.1 [Page 157]

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x^{4}, x = 1, x = 5

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`

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

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

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

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x^{2} + 1, x = 0, x = 3

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

Find the area of the region bounded by the parabola y^{2} = 4x and the line x = 3.

Find the area of circle x^{2} + y^{2} = 25.

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

### 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]

**Choose the correct alternative :**

Area of the region bounded by the curve x^{2} = 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

**Choose the correct alternative :**

The area of the region bounded by y^{2} = 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"`

**Choose the correct alternative :**

Area of the region bounded by x^{2} = 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"`

**Choose the correct alternative :**

Area of the region bounded by y = x^{4}, 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"`

**Choose the correct alternative :**

Using definite integration, area of circle x^{2} + y^{2} = 25 is _______.

5π sq. units

4π sq. units

25π sq. units

25 sq. units

**Fill in the blank :**

Area of the region bounded by y = x^{4}, x = 1, x = 5 and the X-axis is _______.

Using definite integration, area of the circle x^{2} + y^{2} = 49 is _______.

**Fill in the blank :**

Area of the region bounded by x^{2} = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.

**Fill in the blank :**

The area of the region bounded by the curve x^{2} = y, the X-axis and the lines x = 3 and x = 9 is _______.

**Fill in the blank :**

The area of the region bounded by y^{2} = 4x, the X-axis and the lines x = 1 and x = 4 is _______.

**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

**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

**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

**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

**State whether the following is True or False :**

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

True

False

**Solve the following :**

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

**Solve the following :**

Find the area between the parabolas y^{2} = 7x and x^{2} = 7y.

**Solve the following :**

Find the area of the region bounded by the curve y = x^{2} and the line y = 10.

**Solve the following :**

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

**Solve the following :**

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

**Solve the following :**

Find the area of the region bounded by the curve x^{2} = 25y, y = 1, y = 4 and the Y-axis.

**Solve the following :**

Find the area of the region bounded by the parabola y^{2} = 25x and the line x = 5.

## 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

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.

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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.

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