# SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 3 - Application of Definite Integration [Latest edition]

## Chapter 3: Application of Definite Integration

MCQ

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 3 Application of Definite Integration MCQ

#### 2 Marks each

MCQ | Q 1

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

• 16

MCQ | Q 2

The area of the region bounded by the ellipse x2/64 + y2/100 = 1, is ______ sq.units

• 64π

• 80π

• π/80

• 100π

MCQ | Q 3

The area bounded by the parabola y2 = 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

MCQ | Q 4

The area bounded by the curve y2 = x2, and the line x = 8 is ______

• 16 sq.units

• 64 sq.units

• 32 sq.units

• 4 sq.units

MCQ | Q 5

The area of the region included between the parabolas y2 = 16x and x2 = 16y, is given by ______ sq.units

• 256

• 16/3

• 256/3

• 64/3

MCQ | Q 6

The area enclosed between the two parabolas y2 = 20x and y = 2x is ______ sq.units

• 20/3

• 40/3

• 10/3

• 25/3

MCQ | Q 7

The area bounded by the parabola y2 = 32x the X-axis and the latus rectum is ______ sq.units

• 512/3

• 512/5

• 512

• 64/3

MCQ | Q 8

The area bounded by the ellipse x^2/4 + y^2/25 = 1 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)

MCQ | Q 9

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

MCQ | Q 10

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 2022 Chapter 3 Application of Definite Integration Very Short Answers

#### 1 Mark

Very Short Answers | Q 1

Find the area bounded by the curve y2 = 36x, the line x = 2 in first quadrant

Very Short Answers | Q 2

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

Very Short Answers | Q 3

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

Very Short Answers | Q 4

Find the area of the region bounded by the parabola y2 = 32x and its Latus rectum in first quadrant

Very Short Answers | Q 5

Find the area of the region bounded by the curve y = x2, the X−axis and the given lines x = 0, x = 3

Very Short Answers | Q 6

Find the area of the region bounded by the curve y2 = 8x, the X−axis and the given lines x = 1, x = 3, y ≥ 0

Very Short Answers | Q 7

Find the area of the region bounded by the curve x2 = 12y, the Y−axis and the given lines y = 2, y = 4, x ≥ 0

Very Short Answers | Q 8

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

Very Short Answers | Q 9

Find the area of sector bounded by the circle x2 + y2 = 25, in the first quadrant−

Very Short Answers | Q 10

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 2022 Chapter 3 Application of Definite Integration Short Answers I

#### 3 Marks

Short Answers I | Q 1

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

Short Answers I | Q 2

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

Short Answers I | Q 3

Find the area of the region bounded by the parabola y2 = 16x and the line x = 4

Short Answers I | Q 4

Find the area of the region bounded by the curves x2 = 8y, y = 2, y = 4 and the Y-axis, lying in the first quadrant

Short Answers I | Q 5

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

Short Answers I | Q 6

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 2022 Chapter 3 Application of Definite Integration Long Answers II

#### 4 Marks

Long Answers II | Q 1

Find the area of the region bounded by the curves y2 = 4ax and x2 = 4ay

Long Answers II | Q 2

Find the area of the region lying between the parabolas 4y2 = 9x and 3x2 = 16y

Long Answers II | Q 3

Find the area of the sector bounded by the circle x2+ y2 = 16, and the line y = x in the first quadrant

Long Answers II | Q 4

Find the area of the region included between y = x2 + 5 and the line y = x + 7

Long Answers II | Q 5

Find the area enclosed between the circle x2 + y2 = 9, along X-axis and the line x = y, lying in the first quadrant

Long Answers II | Q 6

Find the area enclosed between the circle x2 + y2 = 1 and the line x + y = 1, lying in the first quadrant

Long Answers II | Q 7

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

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 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 2022 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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