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SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 - Definite Integration [Latest edition]

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Chapters

12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 - Shaalaa.com

Chapter 2: Definite 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 2021 Chapter 2 Definite Integration MCQ

2 Marks each

MCQ | Q 1

`int_1^9 (x + 1)/sqrt(x)  "d"x` =

  • `80/3`

  • `64/3`

  • `17/3`

  • `15/3`

MCQ | Q 2

`int_0^1 sqrt((1 - x)/(1 +  x))  "d"x` =

  • `pi/2 - 1`

  • `pi/2 + 1`

  • `pi/2 - 2`

  • `p/2 + 2`

MCQ | Q 3

`int_1^2 ("e"^(1/x))/(x^2)  "d"x` =

  • `2sqrt("e")(1 + sqrt("e"))`

  • `sqrt("e")(1 - sqrt("e"))`

  • `sqrt("e")(sqrt("e") - 1)`

  • `sqrt("e")(1 + sqrt("e"))`

MCQ | Q 4

`int_0^(x/4) sqrt(1 + sin 2x)  "d"x` =

  • `1/sqrt(2)`

  • `sqrt(2) + 1`

  • `2sqrt(2)`

  • 1

MCQ | Q 5

If `int_0^1  ("d"x)/(sqrt(1 + x) - sqrt(x)) = "k"/3`, thn k =

  • `sqrt(2)(2sqrt(2) - 2)`

  • `sqrt(2)/3(2 - 2sqrt(2))`

  • `(2sqrt(2) - )/3`

  • `4sqrt(2)`

MCQ | Q 6

`int_(pi/5)^((3pi)/10)  sinx/(sinx + cosx)  "d"x` =

  • `pi/10`

  • `pi/20`

  • `pi/6`

  • `pi/12`

MCQ | Q 7

`int_0^1 (x^2 - 2)/(x^2 + 1)  "d"x` =

  • `1 - (3pi)/4`

  • `2 - (3pi)/4`

  • `1 + (3pi)/4`

  • `2 + (3pi)/4`

MCQ | Q 8

Let I1 = `int_"e"^("e"^2)  1/logx  "d"x` and I2 = `int_1^2 ("e"^x)/x  "d"x` then 

  • I1 = `1/3 "I"_2`

  • I1 + I2 = 0 

  • I1 = 2I2 

  • I1 = I2 

MCQ | Q 9

`int_0^4 1/sqrt(4x - x^2)  "d"x` =

  • 0

  • π

MCQ | Q 10

`int_0^(pi/2) log(tanx)  "d"x` =

  • `pi/8(log2)`

  • 0

  • `- pi/8 (log2)`

  • `pi/2 (log2)`

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Very Short Answers

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Definite Integration Very Short Answers

1 Mark

Very Short Answers | Q 1

Evaluate: `int_(pi/6)^(pi/3) cosx  "d"x`

Very Short Answers | Q 2

Evaluate: `int_(- pi/4)^(pi/4) x^3 sin^4x  "d"x`

Very Short Answers | Q 3

Evaluate: `int_0^1 1/(1 + x^2)  "d"x`

Very Short Answers | Q 4

Evaluate: `int_0^(pi/4) sec^2 x  "d"x`

Very Short Answers | Q 5

Evaluate: `int_0^1 |x|  "d"x`

Very Short Answers | Q 6

Evaluate: `int_0^1 1/sqrt(1 - x^2)  "d"x`

Very Short Answers | Q 7

Evaluate: `int_1^2 x/(1 + x^2)  "d"x`

Very Short Answers | Q 8

Evaluate: `int_0^1 ""^x/sqrt("e"^x - 1)  "d"x`

Very Short Answers | Q 9

Evaluate: `int_0^(pi/2)  (sin2x)/(1 +  sin^2x)  "d"x`

Very Short Answers | Q 10

Evaluate: `int_0^1(x + 1)^2  "d"x`

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Short Answers I

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Definite Integration Short Answers I

2 Marks

Short Answers I | Q 1

Evaluate: `int_(pi/6)^(pi/3) sin^2 x  "d"x`

Short Answers I | Q 2

Evaluate: `int_0^(pi/2) sqrt(1 - cos 4x)  "d"x`

Short Answers I | Q 3

Evaluate: `int_0^(pi/2) cos^2x  "d"x`

Short Answers I | Q 4

Evaluate: `int_0^pi cos^2 x  "d"x`

Short Answers I | Q 5

Evaluate: `int_0^(pi/4) (tan^3x)/(1 + cos 2x)  "d"x`

Short Answers I | Q 6

Evaluate: `int_0^(pi/4)  cosx/(4 - sin^2 x)  "d"x`

Short Answers I | Q 7

Evaluate: `int_1^3 (cos(logx))/x  "d"x`

Short Answers I | Q 8

Evaluate: `int_0^(pi/2) (sin^2x)/(1 + cos x)^2 "d"x`

Short Answers I | Q 9

Evaluate: `int_0^9 sqrt(x)/(sqrt(x) + sqrt(9) - x)  "d"x`

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Short Answers II

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Definite Integration Short Answers II

3 Marks

Short Answers II | Q 1

Prove that: `int_"a"^"b" "f"(x)  "d"x = int_"a"^"c""f"(x)  "d"x + int_"c"^"b"  "f"(x)  "d"x`, where a < c < b

Short Answers II | Q 2

Prove that: `int_"a"^"b" "f"(x)  "d"x = int_"a"^"b" "f"("a" + "b" - x)  "d"x`

Short Answers II | Q 3

Prove that: `int_0^"a" "f"(x)  "d"x = int_0^"a" "f"("a" - x)  "d"x`. Hence find `int_0^(pi/2) sin^2x  "d"x` 

Short Answers II | Q 4

Evaluate: `int_0^(pi/2) (sin^4x)/(sin^4x + cos^4x)  "d"x`

Short Answers II | Q 5

Evaluate: `int_3^8 (11 - x)^2/(x^2 + (11 - x)^2)  "d"x`

Short Answers II | Q 6

Evaluate: `int_(-1)^1 |5x - 3|  "d"x`

Short Answers II | Q 7

Evaluate: `int_(-4)^2 1/(x^2 + 4x + 13)  "d"x`

Short Answers II | Q 8

Evaluate: `int_0^1 1/sqrt(3 + 2x - x^2)  "d"x`

Short Answers II | Q 9

Evaluate: `int_0^1 x* tan^-1x  "d"x`

Short Answers II | Q 10

Evaluate: `int_0^(1/sqrt(2)) (sin^-1x)/(1 - x^2)^(3/2)  "d"x`

Short Answers II | Q 11

Evaluate: `int_0^(pi/4) sec^4x  "d"x`

Short Answers II | Q 12

Evaluate: `int_0^(pi/2) 1/(5 + 4cos x)  "d"x`

Short Answers II | Q 13

Evaluate: `int_0^(pi/2) cos x/((1 + sinx)(2 + sinx))  "d"x`

Short Answers II | Q 14

Evaluate: `int_(-1)^1 1/("a"^2"e"^x + "b"^2"e"^(-x))  "d"x`

Short Answers II | Q 15

Evaluate: `int_0^"a" 1/(x + sqrt("a"^2 - x^2))  "d"x`

Short Answers II | Q 16

Evaluate: `int_0^3 x^2 (3 - x)^(5/2)  "d"x`

Short Answers II | Q 17

Evaluate: `int_0^1 "t"^2 sqrt(1 - "t")  "dt"`

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Long Answers III

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Definite Integration Long Answers III

4 Marks

Long Answers III | Q 1

Prove that: `int_0^(2"a") "f"(x)  "d"x = int_0^"a" "f"(x)  "d"x + int_0^"a" "f"(2"a" - x)  "d"x`

Long Answers III | Q 2

Prove that: `int_(-"a")^"a" "f"(x)  "d"x` `{:(= 2 int_0^"a" "f" (x)  "d"x ",",  "If"  "f"(x)  "is even function"),(= 0",", "if"  "f"(x)  "is odd function"):}`

Long Answers III | Q 3

Evaluate: `int_0^(1/2) 1/((1 - 2x^2) sqrt(1 - x^2))  "d"x`

Long Answers III | Q 4

Evaluate: `int_0^(pi/4)  (sec^2x)/(3tan^2x + 4tan x + 1)  "d"x`

Long Answers III | Q 5

Evaluate: `int_(1/sqrt(2))^1  (("e"^(cos^-1x))(sin^-1x))/sqrt(1 - x^2)  "d"x`

Long Answers III | Q 6

Evaluate: `int_0^1 (log(x + 1))/(x^2 + 1)  "d"x`

Long Answers III | Q 7

Evaluate: `int_0^pi x*sinx*cos^2x* "d"x`

Long Answers III | Q 8

Evaluate: `int_0^(pi/2)x  sinx  "d"x`

Long Answers III | Q 9

Evaluate: `int_(-1)^1 (1 + x^2)/(9 - x^2)  "d"x`

Long Answers III | Q 10

Evaluate: `int_0^1 (1/(1 + x^2)) sin^-1 ((2x)/(1 + x^2))  "d"x`

Long Answers III | Q 11

Evaluate: `int_0^(pi/4)  (cos2x)/(1 + cos 2x + sin 2x)  "d"x`

Long Answers III | Q 12

Evaluate: `int_0^(pi/4) log(1 + tanx)  "d"x`

Long Answers III | Q 13

Evaluate: `int_0^pi 1/(3 + 2sinx + cosx)  "d"x`

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Chapter 2: Definite Integration

MCQVery Short AnswersShort Answers IShort Answers IILong Answers III
12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 - Definite Integration

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 (Definite 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 2021 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. SCERT Maharashtra Question Bank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 Definite Integration are Definite Integral as Limit of Sum, Fundamental Theorem of Integral Calculus, Methods of Evaluation and Properties of Definite Integral.

Using SCERT Maharashtra Question Bank 12th Board Exam solutions Definite 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 Definite Integration 12th Board Exam extra questions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 and can use Shaalaa.com to keep it handy for your exam preparation

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