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![Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ chapter 5 - Integration - Shaalaa.com](/images/mathematics-and-statistics-1-commerce-english-standard-12-maharashtra-state-board_6:3c1ce41c47804fedaede5f3c658526e1.JPG "Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ chapter 5 - Integration")
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Solutions for Chapter 5: Integration
Below listed, you can find solutions for Chapter 5 of Maharashtra State Board Balbharati for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ.
Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 5 Integration EXERCISE 5.1 [Page 119]
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate `int 1/("x" ("x" - 1))` dx
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 5 Integration EXERCISE 5.2 [Pages 122 - 123]
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 5 Integration EXERCISE 5.3 [Page 123]
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 5 Integration EXERCISE 5.4 [Page 129]
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 5 Integration EXERCISE 5.5 [Page 133]
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int x^2 e^4x`dx
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate the following.
`int "x"^3 "e"^("x"^2)`dx
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 5 Integration EXERCISE 5.6 [Page 135]
Evaluate: `int (2"x" + 1)/(("x + 1")("x - 2"))` dx
Evaluate:
`int (2x + 1)/(x(x - 1)(x - 4)) dx`.
Evaluate: `int ("x"^2 + "x" - 1)/("x"^2 + "x" - 6)` dx
Evaluate:
`int x/((x - 1)^2(x + 2)) dx`
Evaluate: `int "3x - 2"/(("x + 1")^2("x + 3"))` dx
Evaluate: `int 1/("x"("x"^5 + 1))` dx
Evaluate: `int 1/("x"("x"^"n" + 1))` dx
Evaluate: `int (5"x"^2 + 20"x" + 6)/("x"^3 + 2"x"^2 + "x")` dx
Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ 5 Integration MISCELLANEOUS EXERCISE - 5 [Pages 137 - 139]
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
`2sqrt(1 - "x") + "c"`
- `2sqrt(1 - "x") + "c"`
`sqrt"x"` + c
x + c
`int sqrt(1 + "x"^2) "dx"` =
`"x"/2 sqrt(1 + "x"^2) + 1/2 log ("x" + sqrt(1 + "x"^2))`+ c
`2/3 (1 + "x"^2)^(3/2) + "c"`
`1/3 (1 + "x"^2)` + c
`("(x)")/sqrt(1 + "x"^2)` + c
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
`(3)^("x"^3) + "c"`
`(3)^("x"^3)/(3 * log 3) + "c"`
`log 3 (3)^("x"^3)` + c
`"x"^2 (3)^("x"^3) + "c"`
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
`1/3`
`1/2`
`1/4`
2
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
log x – log (1 – x) + c
log (1 - x2) + c
- log x + log(1 - x) + c
log (x - x2) + c
`int "dx"/(("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
`1/15 log |("x" + 2)/("x"+ 1)| + "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 + 3 log "x" - 1/"2x"^2 + "c"`
`"x"^4/4 + "3x"^2/2 + 3 log "x" + 1/"x"^2 + "c"`
`("x" - "x"^-1)^3` + c
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
`"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"`
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
`(1 + "x")^-1` + c
`(1 - "x")^-1` + c
`(1 - "x")^-1 - 1` + c
`(1 - "x")^-1 + 1` + c
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
`(-1)/"x + 1"` + c
`((-1)/"x + 1")^5` + c
log(x + 1) + c
log |x + 1|5 + c
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
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 ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
True
False
State whether the following statement is True or False.
If `int (("x - 1") "dx")/(("x + 1")("x - 2"))` = A log |x + 1| + B log |x - 2| + c, then A + B = 1.
True
False
For `int ("x - 1")/("x + 1")^3 "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)2.
True
False
Solve the following:
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate `int 1/((2"x" + 3))` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: ∫ |x| dx if x < 0
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int "dx"/("9x"^2 - 25)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`
Evaluate: `int "dx"/(5 - 16"x"^2)`
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
Evaluate:
∫ (log x)2 dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int "x" * "e"^"2x"` dx
Evaluate: `int log ("x"^2 + "x")` dx
Evaluate: `int "e"^sqrt"x"` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
Evaluate: `int ("3x" - 1)/("2x"^2 - "x" - 1)` dx
Evaluate: `int (2"x"^3 - 3"x"^2 - 9"x" + 1)/("2x"^2 - "x" - 10)` dx
Evaluate: `int (1 + log "x")/("x"(3 + log "x")(2 + 3 log "x"))` dx
Solutions for 5: Integration
Balbharati solutions for माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ chapter 5 - Integration
Shaalaa.com has the Maharashtra State Board Mathematics माठेमटिक्स अँड स्टॅटिस्टिक्स १ (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. Balbharati solutions for Mathematics माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ Maharashtra State Board 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. Balbharati textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ chapter 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.
Using Balbharati माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ solutions 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 Balbharati Solutions are essential questions that can be asked in the final exam. Maximum Maharashtra State Board माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ students prefer Balbharati Textbook Solutions to score more in exams.
Get the free view of Chapter 5, Integration माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ additional questions for Mathematics माठेमटिक्स अँड स्टॅटिस्टिक्स १ (कॉमर्स) [इंग्रजी] इयत्ता १२ महाराष्ट्र राज्य मंडळ Maharashtra State Board, and you can use Shaalaa.com to keep it handy for your exam preparation.
