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Chapters
1.2: Matrices
1.3: Differentiation
1.4: Applications of Derivatives
1.5: Integration
1.6: Definite Integration
▶ 1.7: Application of Definite Integration
1.8: Differential Equation and Applications
2.1: Commission, Brokerage and Discount
2.2: Insurance and Annuity
2.3: Linear Regression
2.4: Time Series
2.5: Index Numbers
2.6: Linear Programming
2.7: Assignment Problem and Sequencing
2.8: Probability Distributions
![SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC chapter 1.7 - Application of Definite Integration - Shaalaa.com](/images/mathematics-and-statistics-commerce-english-12-standard-hsc_6:5f2b1b2038084cf381bfa42c826a928c.jpg "SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC chapter 1.7 - Application of Definite Integration")
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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 for Mathematics and Statistics (Commerce) [English] 12 Standard HSC.
SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC 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 = x3, 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 x2 + y2 = 16 is ______
4π sq.units
4 sq.units
16 sq.units
16π sq.units
Area of the region bounded by the curve x = y2, 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 x2 = 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 y2 = 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 = y4, 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 y2 = 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 solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC 1.7 Application of Definite Integration Q.1 (B)
[1 Mark]
State whether the following statement is True or False:
y2 = 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 x2 = – 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 x2 + y2 = a2
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 solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC 1.7 Application of Definite Integration Q.1 (C)
Fill in the following blanks [1 Mark]
The area bounded by the parabola x2 = 9y and the lines y = 4 and y = 9 in the first quadrant is ______
The area of the circle x2 + y2 = 16 is ______
The area of the region bounded by the curve y2 = 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 = 4x2, and the lines y = 2 and y = 4 is ______
The area of the region bounded by the curve y2 = x and the Y axis in the first quadrant and lines y = 3 and y = 9 is ______
The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______
The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis is ______
SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC 1.7 Application of Definite Integration Q.2
Attempt the following questions [3 Marks]
Find the area of the region bounded by the parabola y2 = 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 = (x2 + 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 x2 = 36y, y = 1 and y = 4, and the positive Y-axis
Find area of the region bounded by the parabola x2 = 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 solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC 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 x2 + y2 = 62
Find the area between the parabolas y2 = 5x and x2 = 5y
Find the area of the circle x2 + y2 = 16
Find area of the ellipse 4x2 + 9y2 = 36
Solutions for 1.7: Application of Definite Integration
SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC chapter 1.7 - Application of Definite Integration
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Concepts covered in Mathematics and Statistics (Commerce) [English] 12 Standard HSC 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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