Advertisements
Online Mock Tests
Chapters
1.2: Matrics
1.3: Trigonometric Functions
1.4: Pair of Lines
1.5: Vectors and Three Dimensional Geometry
1.6: Line and Plane
1.7: Linear Programming Problems
2.1: Differentiation
2.2: Applications of Derivatives
▶ 2.3: Indefinite Integration
2.4: Definite Integration
2.5: Application of Definite Integration
2.6: Differential Equations
2.7: Probability Distributions
2.8: Binomial Distribution
![SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 2.3 - Indefinite Integration - Shaalaa.com](/images/mathematics-and-statistics-arts-and-science-english-12-standard-hsc_6:5f2b1b2038084cf381bfa42c826a928c.jpg "SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 2.3 - Indefinite Integration")
Advertisements
Solutions for Chapter 2.3: Indefinite Integration
Below listed, you can find solutions for Chapter 2.3 of Maharashtra State Board SCERT Maharashtra for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC.
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 2.3 Indefinite Integration MCQ
2 marks
`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"`
`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
`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"`
`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"`
`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"`
`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
`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"`
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`
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
`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"`
`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"`
`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
`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"`
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
`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 solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 2.3 Indefinite Integration Very Short Answers
1 Mark
`int sqrt(1 + sin2x) "d"x`
`int (sin4x)/(cos 2x) "d"x`
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
`int logx/x "d"x`
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int x^x (1 + logx) "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int (cos2x)/(sin^2x) "d"x`
`int (cos 2x)/(sin x + cos x)^2 "d"x`
`int cot^2x "d"x`
`int x/(x + 2) "d"x`
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 2.3 Indefinite Integration Short Answers I
2 Marks
`int (sinx)/(1 + sin x) "d"x`
`int (2x - 7)/sqrt(4x- 1) dx`
`int 1/(4x + 5x^(-11)) "d"x`
`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int cos^7 x "d"x`
`int x^7/(1 + x^4)^2 "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
`int(log(logx))/x "d"x`
`int x^2sqrt("a"^2 - x^6) "d"x`
`int sqrt(4^x(4^x + 4)) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int sin4x cos3x "d"x`
`int ("e"^xlog(sin"e"^x))/(tan"e"^x) "d"x`
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 2.3 Indefinite Integration Short Answers II
3 Marks
`int 1/(x(x^3 - 1)) "d"x`
If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)
`int ((x^2 + 2))/(x^2 + 1) "a"^(x + tan^(-1_x)) "d"x`
`int (7 + 4x + 5x^2)/(2x + 3)^(3/2) dx`
`int sqrt((9 + x)/(9 - x)) "d"x`
`int 1/(4x^2 - 20x + 17) "d"x`
`int (sinx)/(sin3x) "d"x`
`int 1/(2 + cosx - sinx) "d"x`
`int sec^3x "d"x`
`int sin(logx) "d"x`
`int sec^2x sqrt(tan^2x + tanx - 7) "d"x`
`int "e"^(sin^(-1_x))[(x + sqrt(1 - x^2))/sqrt(1 - x^2)] "d"x`
`int "e"^x ((1 + x^2))/(1 + x)^2 "d"x`
`int (x^2 + x -1)/(x^2 + x - 6) "d"x`
`int (6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1) "d"x`
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 2.3 Indefinite Integration Long Answers III
4 Marks
`int ("d"x)/(2 + 3tanx)`
`int sqrt(tanx) + sqrt(cotx) "d"x`
`int (3x + 4)/sqrt(2x^2 + 2x + 1) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int x^3tan^(-1)x "d"x`
`int x sin2x cos5x "d"x`
`int (x + sinx)/(1 - cosx) "d"x`
`int x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3)) "d"x`
`int ("d"x)/(x^3 - 1)`
Evaluate:
`int (5e^x)/((e^x + 1)(e^(2x) + 9)) dx`
`int 1/(sinx(3 + 2cosx)) "d"x`
`int xcos^3x "d"x`
`int (sin2x)/(3sin^4x - 4sin^2x + 1) "d"x`
`int (3"e"^(2x) + 5)/(4"e"^(2x) - 5) "d"x`
`int ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1]) "d"x`
Solutions for 2.3: Indefinite Integration
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 2.3 - Indefinite Integration
Shaalaa.com has the Maharashtra State Board Mathematics Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 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. SCERT Maharashtra solutions for Mathematics Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC Maharashtra State Board 2.3 (Indefinite 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. SCERT Maharashtra textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 2.3 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 Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC solutions Indefinite 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 SCERT Maharashtra Solutions are essential questions that can be asked in the final exam. Maximum Maharashtra State Board Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC students prefer SCERT Maharashtra Textbook Solutions to score more in exams.
Get the free view of Chapter 2.3, Indefinite Integration Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC additional questions for Mathematics Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC Maharashtra State Board, and you can use Shaalaa.com to keep it handy for your exam preparation.
