#### Chapters

Chapter 1.2: Matrics

Chapter 1.3: Trigonometric Functions

Chapter 1.4: Pair of Lines

Chapter 1.5: Vectors and Three Dimensional Geometry

Chapter 1.6: Line and Plane

Chapter 1.7: Linear Programming Problems

Chapter 2.1: Differentiation

Chapter 2.2: Applications of Derivatives

Chapter 2.3: Indefinite Integration

Chapter 2.4: Definite Integration

Chapter 2.5: Application of Definite Integration

Chapter 2.6: Differential Equations

Chapter 2.7: Probability Distributions

Chapter 2.8: Binomial Distribution

## Chapter 3: Application of Definite Integration

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 3 Application of Definite Integration MCQ

#### 2 Marks each

The area of the region bounded by the curve y = sinx, X-axis and the lines x = 0, x = 4π is ______ sq.units

2

4

8

16

The area of the region bounded by the ellipse x^{2}/64 + y^{2}/100 = 1, is ______ sq.units

64π

80π

`π/80`

100π

The area bounded by the parabola y^{2} = x along the X-axis and the lines x = 0, x = 2 is ______ sq.units

`4/3`

`(4sqrt(2))/3`

`2/3`

`(2sqrt(2))/3`

The area bounded by the curve y^{2} = x^{2}, and the line x = 8 is ______

16 sq.units

64 sq.units

32 sq.units

4 sq.units

The area of the region included between the parabolas y^{2} = 16x and x^{2} = 16y, is given by ______ sq.units

256

`16/3`

`256/3`

`64/3`

The area enclosed between the two parabolas y^{2} = 20x and y = 2x is ______ sq.units

`20/3`

`40/3`

`10/3`

`25/3`

The area bounded by the parabola y^{2} = 32x the X-axis and the latus rectum is ______ sq.units

`512/3`

`512/5`

512

`64/3`

The area bounded by the ellipse `x^2/4 + y^2/25` = 1 and and the line `x/2 + y/5` = 1 is ______ sq.units

5(π – 2)

`5/2(π - 2)`

`5/3(π- 2)`

`5/4(π - 2)`

The area of triangle ΔABC whose vertices are A(1, 1), B(2, 1) and C(3, 3) is ______ sq.units

1

2

3

4

The area enclosed by the line 2x + 3y = 6 along X-axis and the lines x = 0, x = 3 is ______ sq.units

1

2

3

4

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 3 Application of Definite Integration Very Short Answers

#### 1 Mark

Find the area bounded by the curve y^{2} = 36x, the line x = 2 in first quadrant

Find the area bounded by the curve y = sin x, the lines x = 0 and x = `pi/2`

Find the area enclosed between y = cos x and X-axis between the lines x = `pi/2` and x ≤ `(3pi)/2`

Find the area of the region bounded by the parabola y^{2} = 32x and its Latus rectum in first quadrant

Find the area of the region bounded by the curve y = x^{2}, the X−axis and the given lines x = 0, x = 3

Find the area of the region bounded by the curve y^{2} = 8x, the X−axis and the given lines x = 1, x = 3, y ≥ 0

Find the area of the region bounded by the curve x^{2} = 12y, the Y−axis and the given lines y = 2, y = 4, x ≥ 0

Find the area of the ellipse `x^2/1 + y^2/4` = 1, in first quadrant

Find the area of sector bounded by the circle x^{2} + y^{2} = 25, in the first quadrant−

Using integration, find the area of the region bounded by the line 2y + x = 8 , X−axis and the lines x = 2 and x = 4

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 3 Application of Definite Integration Short Answers I

#### 3 Marks

Find the area enclosed between the X-axis and the curve y = sin x for values of x between 0 to 2π

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

Find the area of the region bounded by the parabola y^{2} = 16x and the line x = 4

Find the area of the region bounded by the curves x^{2} = 8y, y = 2, y = 4 and the Y-axis, lying in the first quadrant

Find the area of the region bounded by the curve y = sin x, the X−axis and the given lines x = − π, x = π

Find the area of the ellipse `x^2/36 + y^2/64` = 1, using integration

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 3 Application of Definite Integration Long Answers II

#### 4 Marks

Find the area of the region bounded by the curves y^{2} = 4ax and x^{2} = 4ay

Find the area of the region lying between the parabolas 4y^{2} = 9x and 3x^{2} = 16y

Find the area of the sector bounded by the circle x^{2}+ y^{2} = 16, and the line y = x in the first quadrant

Find the area of the region included between y = x^{2} + 5 and the line y = x + 7

Find the area enclosed between the circle x^{2} + y^{2} = 9, along X-axis and the line x = y, lying in the first quadrant

Find the area enclosed between the circle x^{2} + y^{2} = 1 and the line x + y = 1, lying in the first quadrant

Find the area of the region bounded by the curve (y − 1)^{2} = 4(x + 1) and the line y = (x − 1)

## Chapter 3: Application of Definite Integration

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 3 - Application of Definite Integration

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 3 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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