Advertisements
Online Mock Tests
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 1.6 - Definite 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 1.6 - Definite Integration")
Advertisements
Solutions for Chapter 1.6: Definite Integration
Below listed, you can find solutions for Chapter 1.6 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 1.6 Definite Integration Q.1
MCQ [1 Mark]
Choose the correct alternative:
`int_2^3 x^4 "d"x` =
`1/2`
`5/2`
`5/211`
`211/5`
Choose the correct alternative:
`int_0^"a" 3x^5 "d"x` = 8, then a =
2
0
`8/3`
a
Choose the correct alternative:
`int_4^9 ("d"x)/sqrt(x)` =
9
4
2
0
`int_0^2 e^x dx` = ______.
e2 – 1
1 – e2
e – 1
1 – e
Choose the correct alternative:
`int_(-2)^3 1/(x + 5) "d"x` =
`log (3/8)`
`log (8/3)`
`log (8/5)`
0
Choose the correct alternative:
`int_2^3 x/(x^2 - 1) "d"x` =
`log (8/3)`
`- log (8/3)`
`1/2 log(8/3)`
`-1/2 log(8/3)`
`int_"a"^"b" "f"(x) "d"x` = ______
`int_"b"^"a" "f"(x) "d"x`
`- int_"a"^"b" "f"(x) "d"x`
`- int_"b"^"a" "f"(x) "d"x`
`int_0^"a" "f"(x) "d"x`
`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x)) dx` = ______.
`7/2`
`5/2`
7
2
Choose the correct alternative:
`int_(-9)^9 x^3/(4 - x^2) "d"x` =
0
3
9
– 9
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 1.6 Definite Integration Q.2
Fill in the blanks [1 Mark]
`int_1^2 x^2 "d"x` = ______
`int_0^"a" 4x^3 "d"x` = 81, then a = ______
`int_0^1 "e"^(2x) "d"x` = ______
`int_1^2 1/(2x + 3) dx` = ______
`int_2^4 x/(x^2 + 1) "d"x` = ______
`int_(-7)^7 x^3/(x^2 + 7) "d"x` = ______
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 1.6 Definite Integration Q.3
[1 Mark]
State whether the following statement is True or False:
`int_0^"a" 3x^2 "d"x` = 27, then a = 2.5
True
False
State whether the following statement is True or False:
`int_0^1 1/(2x + 5) "d"x = log(7/5)`
True
False
State whether the following statement is True or False:
`int_2^3 x/(x^2 + 1) "d"x = 1/2 log 2`
True
False
State whether the following statement is True or False:
`int_"a"^"b" "f"(x) "d"x = int_"a"^"b" "f"("a" + "b" - x) "d"x`
True
False
State whether the following statement is True or False:
`int_0^(2"a") "f"(x) "d"x = int_0^"a" "f"(x) "d"x + int_0^"a" "f"("a" - x) "d"x`
True
False
State whether the following statement is True or False:
`int_(-5)^5 x/(x^2 + 7) "d"x` = 10
True
False
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 1.6 Definite Integration Q.4
Solve the following [3 Marks]
Evaluate `int_0^1 (x^2 + 3x + 2)/sqrt(x) "d"x`
Evaluate `int_0^1 1/(sqrt(1 + x) + sqrt(x)) "d"x`
If `int_0^"a" (2x + 1) "d"x` = 2, find a
If `int_1^"a" (3x^2 + 2x + 1) "d"x` = 11, find the real value of a
Evaluate `int_1^"e" 1/(x(1 + log x)^2) "d"x`
Evaluate:
`int_1^2 1/(x^2 + 6x + 5) dx`
Evaluate `int_1^2 (3x)/((9x^2 - 1)) "d"x`
Evaluate the following integrals:
`int_1^3 (root(3)(x + 5))/(root(3)(x + 5) + root(3)(9 - x))*dx`
Evaluate `int_1^2 (sqrt(x))/(sqrt(3 - x) + sqrt(x)) "d"x`
Evaluate the following integrals : `int_0^1 log(1/x - 1)*dx`
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 1.6 Definite Integration Q.5
[4 Marks]
Evaluate `int_2^3 x/((x + 2)(x + 3)) "d"x`
Evaluate `int_1^2 "e"^(2x) (1/x - 1/(2x^2)) "d"x`
Evaluate:
`int_1^3 log x dx`
Evaluate `int_1^3 x^2*log x "d"x`
Evaluate `int_0^1 "e"^(x^2)*"x"^3 "d"x`
Evaluate `int_0^"a" x^2 ("a" - x)^(3/2) "d"x`
Evaluate `int_0^1 x(1 - x)^5 "d"x`
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 1.6 Definite Integration Q.6
Activity [4 Marks]
By completing the following activity, Evaluate `int_1^2 (x + 3)/(x(x + 2)) "d"x`
Solution: Let I = `int_1^2 (x + 3)/(x(x + 2)) "d"x`
Let `(x + 3)/(x(x + 2)) = "A"/x + "B"/((x + 2))`
∴ x + 3 = A(x + 2) + B.x
∴ A = `square`, B = `square`
∴ I = `int_1^2[("( )")/x + ("( )")/((x + 2))] "d"x`
∴ I = `[square log x + square log(x + 2)]_1^2`
∴ I = `square`
By completing the following activity, Evaluate `int_2^5 (sqrt(x))/(sqrt(x) + sqrt(7 - x)) "d"x`.
Solution: Let I = `int_2^5 (sqrt(x))/(sqrt(x) + sqrt(7 - x)) "d"x` ......(i)
Using the property, `int_"a"^"b" "f"(x) "d"x = int_"a"^"b" "f"("a" + "b" - x) "d"x`, we get
I = `int_2^5 ("( )")/(sqrt(7 - x) + "( )") "d"x` ......(ii)
Adding equations (i) and (ii), we get
2I = `int_2^5 (sqrt(x))/(sqrt(x) - sqrt(7 - x)) "d"x + ( ) "d"x`
2I = `int_2^5 (("( )" + "( )")/("( )" + "( )")) "d"x`
2I = `square`
∴ I = `square`
Solutions for 1.6: Definite Integration
SCERT Maharashtra solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ chapter 1.6 - Definite 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 1.6 (Definite 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 1.6 Definite Integration are Overview of Definite Integration.
Using SCERT Maharashtra माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ solutions Definite Integration exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in SCERT Maharashtra Solutions are essential questions that can be asked in the final exam. Maximum Maharashtra State Board माठेमटिक्स अँड स्टॅटिस्टिक्स (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ students prefer SCERT Maharashtra Textbook Solutions to score more in exams.
Get the free view of Chapter 1.6, Definite 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.
