# Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 7 - Applications of Definite Integration [Latest edition]

#### Chapters ## Chapter 7: Applications of Definite Integration

Exercise 7.1Miscellaneous Exercise 7
Exercise 7.1 [Page 157]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 7 Applications of Definite IntegrationExercise 7.1 [Page 157]

Exercise 7.1 | Q 1.1 | Page 157

Find the area of the region bounded by the following curves, the X-axis and the given lines:  y = x4, x = 1, x = 5

Exercise 7.1 | Q 1.2 | Page 157

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

Exercise 7.1 | Q 1.3 | Page 157

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

Exercise 7.1 | Q 1.4 | Page 157

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

Exercise 7.1 | Q 1.5 | Page 157

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

Exercise 7.1 | Q 1.6 | Page 157

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x2 + 1, x = 0, x = 3

Exercise 7.1 | Q 1.7 | Page 157

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = 2 – x2, x = – 1, x = 1

Exercise 7.1 | Q 2 | Page 157

Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.

Exercise 7.1 | Q 3 | Page 157

Find the area of circle x2 + y2 = 25.

Exercise 7.1 | Q 4 | Page 157

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

Miscellaneous Exercise 7 [Pages 157 - 158]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 7 Applications of Definite IntegrationMiscellaneous Exercise 7 [Pages 157 - 158]

Miscellaneous Exercise 7 | Q 1.1 | Page 157

Choose the correct alternative :

Area of the region bounded by the curve x2 = 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

Miscellaneous Exercise 7 | Q 1.2 | Page 157

Choose the correct alternative :

The area of the region bounded by y2 = 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"

Miscellaneous Exercise 7 | Q 1.3 | Page 157

Choose the correct alternative :

Area of the region bounded by x2 = 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"

Miscellaneous Exercise 7 | Q 1.4 | Page 157

Choose the correct alternative :

Area of the region bounded by y = x4, 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"

Miscellaneous Exercise 7 | Q 1.5 | Page 157

Choose the correct alternative :

Using definite integration, area of circle x2 + y2 = 25 is _______.

• 5π sq. units

• 4π sq. units

• 25π sq. units

• 25 sq. units

Miscellaneous Exercise 7 | Q 2.1 | Page 158

Fill in the blank :

Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.

Miscellaneous Exercise 7 | Q 2.2 | Page 158

Using definite integration, area of the circle x2 + y2 = 49 is _______.

Miscellaneous Exercise 7 | Q 2.3 | Page 158

Fill in the blank :

Area of the region bounded by x2 = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.

Miscellaneous Exercise 7 | Q 2.4 | Page 158

Fill in the blank :

The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 is _______.

Miscellaneous Exercise 7 | Q 2.5 | Page 158

Fill in the blank :

The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.

Miscellaneous Exercise 7 | Q 3.1 | Page 158

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

Miscellaneous Exercise 7 | Q 3.2 | Page 158

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

Miscellaneous Exercise 7 | Q 3.3 | Page 158

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

Miscellaneous Exercise 7 | Q 3.4 | Page 158

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

Miscellaneous Exercise 7 | Q 3.5 | Page 158

State whether the following is True or False :

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

• True

• False

Miscellaneous Exercise 7 | Q 4.1 | Page 158

Solve the following :

Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c.

Miscellaneous Exercise 7 | Q 4.2 | Page 158

Solve the following :

Find the area between the parabolas y2 = 7x and x2 = 7y.

Miscellaneous Exercise 7 | Q 4.3 | Page 158

Solve the following :

Find the area of the region bounded by the curve y = x2 and the line y = 10.

Miscellaneous Exercise 7 | Q 4.4 | Page 158

Solve the following :

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

Miscellaneous Exercise 7 | Q 4.5 | Page 158

Solve the following :

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

Miscellaneous Exercise 7 | Q 4.6 | Page 158

Solve the following :

Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.

Miscellaneous Exercise 7 | Q 4.7 | Page 158

Solve the following :

Find the area of the region bounded by the parabola y2 = 25x and the line x = 5.

## Chapter 7: Applications of Definite Integration

Exercise 7.1Miscellaneous Exercise 7 ## 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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