#### Online Mock Tests

#### Chapters

Chapter 1.2: Matrices

Chapter 1.3: Differentiation

Chapter 1.4: Applications of Derivatives

Chapter 1.5: Integration

Chapter 1.6: Definite Integration

▶ Chapter 1.7: Application of Definite Integration

Chapter 1.8: Differential Equation and Applications

Chapter 2.1: Commission, Brokerage and Discount

Chapter 2.2: Insurance and Annuity

Chapter 2.3: Linear Regression

Chapter 2.4: Time Series

Chapter 2.5: Index Numbers

Chapter 2.6: Linear Programming

Chapter 2.7: Assignment Problem and Sequencing

Chapter 2.8: Probability Distributions

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## Solutions for Chapter 1.7: Application of Definite Integration

Below listed, you can find solutions for Chapter 1.7 of Maharashtra State Board SCERT Maharashtra Question Bank for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022.

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.7 Application of Definite Integration Q.1 (A)

#### MCQ [1 Mark]

**Choose the correct alternative:**

Area of the region bounded by the curve y = x^{3}, x = 1, x = 4 and the X-axis is ______

`225/4` sq.units

`256/4` sq.units

`255/3` sq.units

`256/3` sq.units

**Choose the correct alternative:**

Using the definite integration area of the circle x^{2} + y^{2} = 16 is ______

4π sq.units

4 sq.units

16 sq.units

16π sq.units

Area of the region bounded by the curve x = y^{2}, the positive Y axis and the lines y = 1 and y = 3 is ______

26 sq.units

3 sq.units

`3/26` sq.units

`26/3` sq.units

**Choose the correct alternative:**

Area of the region bounded by the curve x^{2} = 8y, the positive Y-axis lying in the first quadrant and the lines y = 4 and y = 9 is ______

`(76sqrt(2))/3` sq.units

`(76sqrt(2))/2` sq.units

`(38sqrt(2))/3` sq.units

`76sqrt(2)` sq.units

**Choose the correct alternative:**

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

`56/3` sq.units

`3/56` sq.units

56 sq.units

63 sq.units

**Choose the correct alternative:**

Area of the region bounded by x = y^{4}, y = 1 and y = 5 and the Y-axis lying in the first quadrant is ______

`3124/5` sq.units

`3142/5` sq.units

`3124/3` sq.units

`3142/3` sq.units

**Choose the correct alternative:**

Area of the region bounded by the parabola y^{2} = 25x and the lines x = 5 is ______

`(75sqrt(5))/2` sq.units

`(20sqrt(5))/3` sq.units

`(100sqrt(5))/3` sq.units

`(75sqrt(5))/3` sq.units

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.7 Application of Definite Integration Q.1 (B)

#### [1 Mark]

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

y^{2} = 4ax is the standard form of parabola when curve lies on X-axis

True

False

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

Standard form of parabola is x^{2} = – 4by, when curve lies in the positive Y-axis

True

False

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

The area of portion lying below the X axis is negative

True

False

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

The area bounded by the curve y = f(x) lies on the both sides of the X-axis is `|int_"a"^"b" "f"(x) "d"x| + |int_"b"^"c" "f"(x) "d"x|`

True

False

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

The equation of the area of the circle is `x^2/"a"^2 + y^2/"b"^2` = 1

True

False

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

The equation of the area of the ellipse is x^{2} + y^{2} = a^{2}

True

False

The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x) "d"x`

True

False

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.7 Application of Definite Integration Q.1 (C)

#### Fill in the following blanks [1 Mark]

The area bounded by the parabola x^{2} = 9y and the lines y = 4 and y = 9 in the first quadrant is ______

The area of the circle x^{2} + y^{2} = 16 is ______

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

The area of the region lying in the first quadrant and bounded by the curve y = 4x^{2}, and the lines y = 2 and y = 4 is ______

The area of the region bounded by the curve y^{2} = x and the Y axis in the first quadrant and lines y = 3 and y = 9 is ______

The area of the region x^{2} = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______

The area of the region bounded by y^{2} = 25x, x = 1 and x = 2 the X axis is ______

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.7 Application of Definite Integration Q.2

#### Attempt the following questions [3 Marks]

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

Find the area of the region bounded by the curve y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3

Find the area of the region bounded by the curve y = `sqrt(2x + 3)`, the X axis and the lines x = 0 and x = 2

Find the area of the region bounded by the curve 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8

Find the area of the region bounded by the curve y = (x^{2} + 2)^{2}, the X-axis and the lines x = 1 and x = 3

Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant

Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2

Find area of the region bounded by the parabola x^{2} = 36y, y = 1 and y = 4, and the positive Y-axis

Find area of the region bounded by the parabola x^{2} = 4y, the Y-axis lying in the first quadrant and the lines y = 3

Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5

Find the area of the region bounded by the curve y = `sqrt(36 - x^2)`, the X-axis lying in the first quadrant and the lines x = 0 and x = 6

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.7 Application of Definite Integration Q.3

#### Attempt the following questions [4 Mark]

Find area of the ellipse `x^2/5^2 + y^2/4^2` = 1

Find the area of the circle x^{2} + y^{2} = 6^{2}^{ }

Find the area between the parabolas y^{2} = 5x and x^{2} = 5y

Find the area of the circle x^{2} + y^{2} = 16

Find area of the ellipse 4x^{2} + 9y^{2} = 36

## Solutions for Chapter 1.7: Application of Definite Integration

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 1.7 - Application of Definite Integration

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 1.7 Application of Definite Integration are Standard Forms of Parabola and Their Shapes, Standard Forms of Ellipse, Area Under Simple Curves.

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