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#### Chapters

Chapter 2: Matrices

Chapter 3: Differentiation

Chapter 4: Applications of Derivatives

Chapter 5: Integration

Chapter 6: Definite Integration

▶ Chapter 7: Applications of Definite Integration

Chapter 8: Differential Equation and Applications

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## Solutions for Chapter 7: Applications of Definite Integration

Below listed, you can find solutions for Chapter 7 of Maharashtra State Board Balbharati for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board.

### 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"`

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

63 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"`

Using definite integration, the area of the 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.

## Solutions for 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

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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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