# 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 ## Chapter 2: Indefinite Integration

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

### 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

### 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

### 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

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

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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.

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