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SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 2 - Indefinite Integration [Latest edition]

Chapters

12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 - Shaalaa.com
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Chapter 2: Indefinite Integration

MCQVery Short AnswersShort Answers IShort Answers IILong Answers III
MCQ

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Indefinite Integration MCQ

2 marks

MCQ | Q 1

`int sqrt(tan x)/(sin x cos x)` dx = _______________

  • `1/2 sqrt(tan x) + "c"`

  • `2 sqrt(tan x) + "c"`

  • `sqrt2 tan x + "c"`

  • `1/sqrt(2 tan x) + "c"`

MCQ | Q 2

`int 1/(sqrtx + sqrt(x^3))` dx = _____________

  • `2 tan^(-1) (sqrtx) + "c"`

  • tan−1 (2x − 1) + c

  • `2 tan sqrtx + "c"`

  • 2 tan−1 (x) + c

MCQ | Q 3

`int 1/sqrt((x - 3)(x - 2))` dx = ________________

  • `1/2 log [(2x - 1) + sqrt(x^2 - x - 6)] + "c"`

  • tan−1 (2x − 1) + c

  • `log [(x - 1/2) + sqrt(x^2 - x - 6)] + "c"`

  • `log [(x - 1/2) + sqrt(x^2 + x + 6)] + "c"`

MCQ | Q 4

`int 1/(cos x - sin x)` dx = _______________

  • `1/sqrt2 log ["cosec" (x + π/4) - cot (x + π/4)] + "c"`

  • `sqrt2 log ["cosec" (x + π/4) + cot (x + π/4)] + "c"`

  • `1/sqrt2 log [sec (x + π/4) + tan (x + π/4)] + "c"`

  • `sqrt2 log [sec (x + π/4) - tan (x + π/4)] + "c"`

MCQ | Q 5

`int x^2/sqrt(1 - x^6)` dx = ________________

  • −sin−1 (x3) + c

  • cos−1 (x3) + c

  • sin−1 (x3) + c

  • `1/3 sin^(-1) (x^3) + "c"`

MCQ | Q 6

`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________

  • ex log x + c

  • ex (log x)2 + c

  • e2x log x + c

  • e2x (log x)2 + c

MCQ | Q 7

`int sqrt(x^2 + 2x + 5)` dx = ______________

  • `(x + 1) sqrt(x^2 + 2x + 5) + log [(x + 1) + sqrt(x^2 + 2x + 5)] + "c"`

  • `(x + 2) sqrt(x^2 + 2x + 5) + log [(x + 2) + sqrt(x^2 + 2x + 5)] + "c"`

  • `(("x" + 2)/2) sqrt(x^2 + 2x + 5) + 1/2 log [(x + 2) + sqrt(x^2 + 2x + 5)] + "c"`

  • `(("x" + 1)/2) sqrt(x^2 + 2x + 5) + 2 log [(x + 1) + sqrt(x^2 + 2x + 5)] + "c"`

MCQ | Q 8

Choose the correct options from the given alternatives :

If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` =

  • `e^(sin^-1x)*(sin^-1 x - 1) + c`

  • `e^(sin^-1x)*(1 - sin^-1x) + c`

  • `e^(sin^-1x)*(sin^-1 x + 1) + c`

  • `-e^(sin^-1x)*(sin^-1 x + 1) + c`

MCQ | Q 9

Choose the correct options from the given alternatives :

`int (sin^m x)/(cos^(m+2)x)*dx` = 

  • `(tan^(m+1)x)/(m + 1) + c`

  • (m + 2)tanm+1 x + c

  • `tan^mx/m + c`

  • (m + 1)tanm+1 x + c

MCQ | Q 10

`int 2/(sqrtx - sqrt(x + 3))` dx = ________________

  • `-2/3 [x^(3/2) + (x + 3)^(3/2)] + "c"`

  • `2/3 [x^(3/2) - (x + 3)^(3/2)] + "c"`

  • `4/9 [x^(3/2) - (x + 3)^(3/2)] + "c"`

  • `-4/9 [x^(3/2) + (x + 3)^(3/2)] + "c"`

MCQ | Q 11

`int cos sqrtx` dx = _____________

  • `2 [sqrtx sin sqrtx + cos sqrtx] + "c"`

  • `sqrtx sin sqrtx + cos sqrtx + "c"`

  • `2 [sqrtx cos sqrtx + sin sqrtx] + "c"`

  • `1/2 [sqrtx sin sqrtx - cos sqrtx] + "c"`

MCQ | Q 12

`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________

  • sin 2x + c

  • cos 2x + c

  • tan 2x + c

  • 2 sin 2x + c

MCQ | Q 13

`int (log x)/(log ex)^2` dx = _________

  • x (1 + log x) + c

  • `x/(1 + log x) + "c"`

  • `1/(1 + log x) + "c"`

  • `1/(1 - log x) + "c"`

MCQ | Q 14

If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______

  • f(x) − log x + c

  • f(x) + log x + c

  • log x − f(x) + c

  • `1/5x^5` f(x) + c

MCQ | Q 15

`int  ("e"^x(x - 1))/(x^2)  "d"x` = ______ 

  • `x"e"^(-x) + c`

  • `("e"^x)/(x^2) + c`

  • `(x - 1/x)"e"^x + c`

  • `("e"^x)/x + c`

Very Short Answers

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Indefinite Integration Very Short Answers

1 Mark

Very Short Answers | Q 1

`int sqrt(1 + sin2x)  "d"x`

Very Short Answers | Q 2

`int (sin4x)/(cos 2x) "d"x`

Very Short Answers | Q 3

`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`

Very Short Answers | Q 4

`int 1/sqrt(3x^2 + 8)  "d"x`

Very Short Answers | Q 5

`int logx/x  "d"x`

Very Short Answers | Q 6

`int (2 + cot x - "cosec"^2x) "e"^x  "d"x`

Very Short Answers | Q 7

`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`

Very Short Answers | Q 8

`int ("e"^(2x) + "e"^(-2x))/("e"^x)  "d"x`

Very Short Answers | Q 9

`int x^x (1 + logx)  "d"x`

Very Short Answers | Q 10

`int 1/(xsin^2(logx))  "d"x`

Very Short Answers | Q 11

`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`

Very Short Answers | Q 12

`int (cos2x)/(sin^2x)  "d"x`

Very Short Answers | Q 13

`int (cos 2x)/(sin x + cos x)^2  "d"x`

Very Short Answers | Q 14

`int cot^2x  "d"x`

Very Short Answers | Q 15

`int x/(x + 2)  "d"x`

Short Answers I

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Indefinite Integration Short Answers I

2 Marks

Short Answers I | Q 1

`int (sinx)/(1 + sin x)  "d"x`

Short Answers I | Q 2

`int ((2x - 7))/sqrt(4x- 1)  "d"x`

Short Answers I | Q 3

`int 1/(4x + 5x^(-11))  "d"x`

Short Answers I | Q 4

`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`

Short Answers I | Q 5

`int (sin(x - "a"))/(cos (x + "b"))  "d"x`

Short Answers I | Q 6

`int cos^7 x  "d"x`

Short Answers I | Q 7

`int x^7/(1 + x^4)^2  "d"x`

Short Answers I | Q 8

`int 1/sqrt(2x^2 - 5)  "d"x`

Short Answers I | Q 9

`int(log(logx))/x  "d"x`

Short Answers I | Q 10

`int x^2sqrt("a"^2 - x^6)  "d"x`

Short Answers I | Q 11

`int sqrt(4^x(4^x + 4))  "d"x`

Short Answers I | Q 12

`int ["cosec"(logx)][1 - cot(logx)]  "d"x`

Short Answers I | Q 13

`int (cos2x)/(sin^2x cos^2x)  "d"x`

Short Answers I | Q 14

`int sin4x cos3x  "d"x`

Short Answers I | Q 15

`int ("e"^xlog(sin"e"^x))/(tan"e"^x)  "d"x`

Short Answers II

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Indefinite Integration Short Answers II

3 Marks

Short Answers II | Q 1

`int 1/(x(x^3 - 1)) "d"x`

Short Answers II | Q 2

If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)

Short Answers II | Q 3

`int ((x^2 + 2))/(x^2 + 1) "a"^(x + tan^(-1_x)) "d"x`

Short Answers II | Q 4

`int (7 + 4x + 5x^2)/(2x + 3)^(3/2)  "d"x`

Short Answers II | Q 5

`int sqrt((9 + x)/(9 - x))  "d"x`

Short Answers II | Q 6

`int 1/(4x^2 - 20x + 17)  "d"x`

Short Answers II | Q 7

`int (sinx)/(sin3x)  "d"x`

Short Answers II | Q 8

`int 1/(2 +  cosx - sinx)  "d"x`

Short Answers II | Q 9

`int sec^2x  "d"x`

Short Answers II | Q 10

`int sin(logx)  "d"x`

Short Answers II | Q 11

`int sec^2x sqrt(tan^2x + tanx - 7)  "d"x`

Short Answers II | Q 12

`int "e"^(sin^(-1_x))[(x + sqrt(1 - x^2))/sqrt(1 - x^2)] "d"x`

Short Answers II | Q 13

`int "e"^x ((1 + x^2))/(1 + x)^2  "d"x`

Short Answers II | Q 14

`int (x^2 + x -1)/(x^2 + x - 6)  "d"x`

Short Answers II | Q 15

`int (6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1)  "d"x`

Long Answers III

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 2 Indefinite Integration Long Answers III

4 Marks

Long Answers III | Q 1

`int ("d"x)/(2 + 3tanx)`

Long Answers III | Q 2

`int sqrt(tanx) + sqrt(cotx)  "d"x`

Long Answers III | Q 3

`int (3x + 4)/sqrt(2x^2 + 2x + 1)  "d"x`

Long Answers III | Q 4

`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1))  "d"x`

Long Answers III | Q 5

`int x^3tan^(-1)x  "d"x`

Long Answers III | Q 6

`int x sin2x cos5x  "d"x`

Long Answers III | Q 7

`int (x + sinx)/(1 - cosx)  "d"x`

Long Answers III | Q 8

`int  x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3))  "d"x`

Long Answers III | Q 9

`int ("d"x)/(x^3 - 1)`

Long Answers III | Q 10

`int (5"e"^x)/(("e"^x + 1)("e"^(2x) + 9))  "d"x`

Long Answers III | Q 11

`int 1/(sinx(3 + 2cosx))  "d"x`

Long Answers III | Q 12

`int xcos^3x  "d"x`

Long Answers III | Q 13

`int (sin2x)/(3sin^4x - 4sin^2x + 1)  "d"x`

Long Answers III | Q 14

`int (3"e"^(2x) + 5)/(4"e"^(2x) - 5)  "d"x`

Long Answers III | Q 15

`int  ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1])  "d"x`

Chapter 2: Indefinite Integration

MCQVery Short AnswersShort Answers IShort Answers IILong Answers III
12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 2 - Indefinite Integration

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 2 (Indefinite Integration) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 2 Indefinite Integration are Indefinite Integration, Methods of Integration: Integration by Substitution, Methods of Integration: Integration by Parts, Methods of Integration: Integration Using Partial Fractions.

Using SCERT Maharashtra Question Bank 12th Board Exam solutions Indefinite Integration exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in SCERT Maharashtra Question Bank Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 12th Board Exam prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exam.

Get the free view of chapter 2 Indefinite Integration 12th Board Exam extra questions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 and can use Shaalaa.com to keep it handy for your exam preparation

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