#### Online Mock Tests

#### Chapters

## Solutions for Chapter 5: Integration

Below listed, you can find solutions for Chapter 5 of Maharashtra State Board Balbharati for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board.

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 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) = x^{2} + 5 and f(0) = −1, then find the value of f(x).

If f '(x) = 4x^{3} - 3x^{2} + 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 Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 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 Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 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 Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 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/(4"x"^2 - 20"x" + 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 Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 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 Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 5 Integration Exercise 5.6 [Page 135]

**Evaluate: **`int (2"x" + 1)/(("x + 1")("x - 2"))` dx

**Evaluate: **`int (2"x" + 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 Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 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

**Choose the correct alternative from the following.**

`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 - x

^{2}) + c- log x + log(1 - x) + c

log (x - x

^{2}) + c

**Choose the correct alternative from the following.**

`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

`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 = x^{4} + ______ x^{3} + 5x + c

`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c

**Fill in the Blank.**

If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______

**Fill in the Blank.**

To find the value of `int ((1 + log "x") "dx")/"x"` 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

**State whether the following statement is True or False.**

For `int ("x - 1")/("x + 1")^3 "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)^{2}.

True

False

**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 Chapter 5: Integration

## Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 5 - Integration

Shaalaa.com has the Maharashtra State Board Mathematics Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board 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 Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board 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 Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 5 Integration are Integration, Methods of Integration: Integration by Substitution, Methods of Integration: Integration by Parts, Methods of Integration: Integration Using Partial Fractions.

Using Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board 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 Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board students prefer Balbharati Textbook Solutions to score more in exams.

Get the free view of Chapter 5, Integration Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board additional questions for Mathematics Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Maharashtra State Board, and you can use Shaalaa.com to keep it handy for your exam preparation.