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Chapters
2: Matrices
3: Differentiation
4: Applications of Derivatives
5: Integration
6: Definite Integration
▶ 7: Applications of Definite Integration
8: Differential Equation and Applications
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Solutions for Chapter 7: Applications of Definite Integration
Below listed, you can find solutions for Chapter 7 of Maharashtra State Board Balbharati for Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board.
Balbharati solutions for Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board 7 Applications of Definite Integration Exercise 7.1 [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
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`
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
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
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
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
Find the area of the region bounded by the following curve, the X-axis and the given line:
y = 2 – x2, x = –1, x = 1
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
Find the area of circle x2 + y2 = 25.
Find the area of ellipse `x^2/(4) + y^2/(25)` = 1.
Balbharati solutions for Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board 7 Applications of Definite Integration Miscellaneous Exercise 7 [Pages 157 - 158]
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
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
`(28)/(3)` sq. units
`(3)/(28)` sq. units
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.
63 sq. units
`(3)/(56)"sq. units"`
`(56)/(3)"sq. units"`
`(63)/(7)"sq. units"`
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"`
Using definite integration, the area of the circle x2 + y2 = 25 is ______.
5π sq.units
4π sq.units
25π sq.units
25 sq.units
Fill in the blank :
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.
Using definite integration, area of the circle x2 + y2 = 49 is _______.
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 _______.
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 _______.
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
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
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
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
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
State whether the following is True or False :
The area of the portion lying above the X-axis is positive.
True
False
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.
Solve the following :
Find the area between the parabolas y2 = 7x and x2 = 7y.
Solve the following :
Find the area of the region bounded by the curve y = x2 and the line y = 10.
Solve the following :
Find the area of the ellipse `x^2/(16) + y^2/(9)` = 1.
Solve the following :
Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5.
Solutions for 7: Applications of Definite Integration
Balbharati solutions for Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board chapter 7 - Applications of Definite Integration
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Concepts covered in Mathematics and Statistics 1 (Commerce) [English] 12 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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