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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 माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ chapter 1.5 - Integration - Shaalaa.com](/images/mathematics-and-statistics-commerce-english-standard-12-maharashtra-state-board_6:5f2b1b2038084cf381bfa42c826a928c.jpg "SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ chapter 1.5 - Integration")
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Solutions for Chapter 1.5: Integration
Below listed, you can find solutions for Chapter 1.5 of Maharashtra State Board SCERT Maharashtra for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ.
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 1.5 Integration Q.1
MCQ [1 Mark]
Choose the correct alternative:
The value of `int ("d"x)/sqrt(1 - x)` is
`2sqrt(1 - x) + "c"`
`-2sqrt(1 - x) + "c"`
`sqrt(x) + "c"`
x + c
Choose the correct alternative:
`int sqrt(1 + x) "d"x` =
`x/2 sqrt(1 + x) + "c"`
`2/3(1 + x)^(3/2) + "c"`
`2/sqrt(1 + x) + "c"`
`(-3)/2 (1 + x) + "c"`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`(3)^(x^3) + "c"`
`((3)^(x^3))/(3log3) + "c"`
`log 3*(3)^(x^3) + "c"`
`x^2 (3)^(x^2) + "c"`
Choose the correct alternative:
`int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x`, then p = ?
`1/3`
`1/2`
`1/4`
2
`int ("d"x)/(x - x^2)` = ______
log x – log(1 – x) + c
log(1 – x2) + c
– log x + log(1 – x) + c
log(x – x2) + c
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
`1/15 log((x + 2)/(x - 1)) + "c"`
`1/15 log((x + 8)/(x + 7)) + "c"`
`1/15 log((x - 8)/(x + 7)) + "c"`
(x – 8)(x – 7) + c
`int(x + 1/x)^3 dx` = ______.
`1/4(x + 1/x)^4 + c`
`x^4/4 + (3x^2)/2 + 3log x - 1/(2x^2) + c`
`x^4/4 + (3x^2)/2 + 3log x + 1/x^2 + c`
`(x - x^(-1))^3 + c`
Choose the correct alternative:
`int(("e"^(2x) + "e"^(-2x))/"e"^x) "d"x` =
`"e"^x - 1/(3"e"^(3x)) + "c"`
`"e"^x + 1/(3"e"^(3x)) + "c"`
`"e"^(-x) - 1/(3"e"^(3x)) + "c"`
`"e"^(-x) + 1/(3"e"^(3x)) + "c"`
`int(1 - x)^(-2) dx` = ______.
(1 − x)−1 + c
(1 + x)−1 + c
(1 − x)−1 − 1 + c
(1 − x)−1 + 1 + c
(1 − x)−1 − x + c
(1 − x)−1 + x + c
Choose the correct alternative:
`int ((x^3 + 3x^2 + 3x + 1))/(x + 1)^5 "d"x` =
`(-1)/(x + 1) + "c"`
`((-1)/(x + 1))^5 + "c"`
log(x + 1) + c
5log(x + 5) + c
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 1.5 Integration Q.2
Fill in the blanks [1 Mark]
`int 1/x "d"x` = ______ + c
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
`int (7x + 9)^13 "d"x` ______ + c
`int"e"^(4x - 3) "d"x` = ______ + c
`int 5^(6x + 9) "d"x` = ______ + c
`int (5(x^6 + 1))/(x^2 + 1) "d"x` = x5 – ______ x3 + 5x + c
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
If f'(x) = `1/x + x` and f(1) = `5/2`, then f(x) = log x + `x^2/2` + ______ + c
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
`int 1/x^3 [log x^x]^2 "d"x` = p(log x)3 + c Then p = ______
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 1.5 Integration Q.3
[1 Mark]
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
True
False
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
True
False
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
True
False
State whether the following statement is True or False:
If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1| + B log|x – 2|, then A + B = 1
True
False
State whether the following statement is True or False:
For `int (x - 1)/(x + 1)^3 "e"^x"d"x` = ex f(x) + c, f(x) = (x + 1)2
True
False
State whether the following statement is True or False:
If f'(x) = 3x2 + 2x, then by definition of integration, we get f(x) = x3 + x2 + c
True
False
If f(x) = k, where k is constant, then `int "k" "d"x` = 0
True
False
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
True
False
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
True
False
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
True
False
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 1.5 Integration Q.4
Solve the following [3 Marks]
Evaluate `int(3x^2 - 5)^2 "d"x`
Evaluate `int 1/(x(x - 1)) "d"x`
Evaluate `int 1/(x log x) "d"x`
Evaluate `int (2"e"^x + 5)/(2"e"^x + 1) "d"x`
Evaluate `int 1/(4x^2 - 1) "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
Evaluate `int x log x "d"x`
Evaluate `int x^2"e"^(4x) "d"x`
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 1.5 Integration Q.5
Evaluate the following [4 Marks]
`int "e"^x x/(x + 1)^2 "d"x`
`int x^3"e"^(x^2) "d"x`
`int x/((x - 1)^2 (x + 2)) "d"x`
`int logx/(1 + logx)^2 "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
`int 1/(4x^2 - 20x + 17) "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
`int (3"e"^(2"t") + 5)/(4"e"^(2"t") - 5) "dt"`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Solutions for 1.5: Integration
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ chapter 1.5 - Integration
Shaalaa.com has the Maharashtra State Board Mathematics माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. SCERT Maharashtra solutions for Mathematics माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ Maharashtra State Board 1.5 (Integration) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. SCERT Maharashtra textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ chapter 1.5 Integration are Integration, Methods of Integration> Integration by Substitution, Methods of Integration> Integration by Parts, Methods of Integration> Integration Using Partial Fraction, Overview of Integration.
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Get the free view of Chapter 1.5, Integration माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ additional questions for Mathematics माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ Maharashtra State Board, and you can use Shaalaa.com to keep it handy for your exam preparation.
