Indefinite Definition and 299 Threads

An indefinite pronoun is a pronoun which does not have a specific familiar referent. Indefinite pronouns are in contrast to definite pronouns.
Indefinite pronouns can represent either count nouns or noncount nouns. They often have related forms across these categories: universal (such as everyone, everything), assertive existential (such as somebody, something), elective existential (such as anyone, anything), and negative (such as nobody, nothing).Many languages distinguish forms of indefinites used in affirmative contexts from those used in non-affirmative contexts. For instance, English "something" can only be used in affirmative contexts while "anything" is used otherwise.Indefinite pronouns are associated with indefinite determiners of a similar or identical form (such as every, any, all, some). A pronoun can be thought of as replacing a noun phrase, while a determiner introduces a noun phrase and precedes any adjectives that modify the noun. Thus all is an indefinite determiner in "all good boys deserve favour" but a pronoun in "all are happy".

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  1. MarkFL

    MHB Luc's question at Yahoo Answers regarding an indefinite integral

    Here is the question: Here is a link to the question: Find the indefinite integral? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  2. K

    Evaluate the indefinite integral as an infinite series

    Homework Statement Evaluate the indefinite integral as an infinite series ∫ sin(x2) dx Homework Equations The Macluarin series of sin x = ∞ Ʃ (-1)nx2n+1/(2n+1)! n=0 The Macluarin series for sin(x2) = ∞ Ʃ (-1)x4n+2/(2n+1)! n=0 The Attempt...
  3. MarkFL

    MHB Thomas' question at Yahoo Answers regarding an indefinite integral

    Here is the question: Here is a link to the question: Calc 2 integral question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  4. B

    Square Root Indefinite Integral

    Hello everyone.. Homework Statement ∫√((1+(e^-x))^2)dx 2. The attempt at a solution I first tried to do a u sub and then attempt a trig sub however I can't do anything with the e^-x left in the u sub. Does anyone have another way I can integrate this thing?? Thank you for any suggestions/help!
  5. MarkFL

    MHB LP_Rocks' question at Yahoo Answers regarding an indefinite integral

    Here is the question: Here is a link to the question: Integration question!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  6. H

    Finding the sum of an indefinite series

    Homework Statement Ʃ(x-->infinity, x>0) 11/(n(n+2)) Homework Equations The Attempt at a Solution I am not quite sure what to do, i think that i am supposed to put it into partial fractions. i changed it to the form 11/(n^2+2n) --> 11/((n+1)(n+1)-1)) --> 11/((n+1)^2-1)...
  7. D

    Antiderivative and Indefinite Integration

    Homework Statement ∫(x3 - 3x2 + x + 1)/√x dx The Attempt at a Solution ∫x3-1/2 - 3∫x2-1/2 + ∫x1-1/2 + ∫x1-1/2 ∫x5/2 - 3∫x3/2 + ∫x1/2 + ∫1/2 (x7/2)7/2 - (3x5/2)5/2 + (x3/2)3/2 + (x3/2)3/2 + C (2x7/2)/7 - (6x5/2)/5 + 2x3/2)/3 + (2x3/2)/3 + C Thank you so much!
  8. S

    Indefinite Integral of (3x^2-10)/(x^2-4x+4) dx using PARTIAL FRACTION

    Homework Statement Integrate (3x^2-10)/(x^2-4x+4) dx using partial fractions. Homework Equations None The Attempt at a Solution I tried using A/(x-2) + B/(x-2)^2 but I didnt get a coeffecient of an x^2. I've also tried using (Ax+B)/(x-2) + C/(x-2)^2 Though I...
  9. C

    Calc II homework - substitution of definite and indefinite integrals

    It's been a year since I took Calc I, and I'm taking Calc II online this semester. This is technically a review problem from Calc I, and I managed the other seven, but I can't figure out how to solve this problem. 1.a Homework Statement ∫(a*sin(14x))/(\sqrt{1-196x^2} dx, evaluated at x=0...
  10. K

    How to Find the Indefinite Integral for (4x^2+2√x+1)/(2x√x)?

    Homework Statement ∫▒〖(4x^2+2√x+1)/(2x√x) dx〗 Homework Equations The Attempt at a Solution ∫▒〖(4x^2+2√x+1)/(2x√x) dx〗 ∫▒((4x^2)/(2x^(3/2) )+(2√x)/(2x^(3/2) )+1/(2x^(3/2) ))dx 2∫▒x^(1/2) dx+∫▒〖x^(-1) dx〗+1/2 ∫▒x^(-3/2) dx 2×2/3 x^(3/2)+ln⁡x+1/2×(-2) x^(-1/2)+C 4/3...
  11. H

    Difficult indefinite integral (mix of integration by parts and/or substitution)

    Homework Statement I do not know how to solve the following indefinite integral. I personally think it is very difficult and would appreciate it had someone can explain it step by step? Homework Equations / The Attempt at a Solution This integral must been solved by mix of...
  12. T

    Connection between definite and indefinite integrals?

    I understand that the indefinite integral is like infinite definite integrals, but how come when we calculate the definite integral we simply substitute the two values into the indefinite integral and subtract? Why do we subtract? Why not add? Also, there aren't the same thing, right? What's...
  13. Kushwoho44

    Order of Indefinite Double Integrals

    Hi, Rather simple question here, just want to confirm: When we are dealing with indefinite double integrals, it's true to say ∫∫ f(x,y) dx dy = ∫∫ f(x,y) dy dx i.e, order of integration doesn't matter right?
  14. G

    Finding the Indefinite Integral of a Product of Exponential Functions

    Homework Statement F(x)= (3^x)(e^x)dx Homework Equations F(u)=U^n=(U^(n+1))/n+1 The Attempt at a Solution I said it equaled: ((3^(x+1))/(x+1))(e^x)
  15. J

    MHB Integral of $\sqrt{\frac{x^2+1}{x^2-1}}$

    $\displaystyle \int\sqrt{\frac{x^2+1}{x^2-1}}dx$
  16. H

    Why can't the indefinite integral be written with sigma notation?

    Hi, I've been wondering this since I started learning integration. I get that ∫ is basically an elongated S for "sum", because that is what it is basically doing. But then Ʃ does the same thing as well. If I'm understanding the difference, it is that Ʃ increments by finite measures, whereas ∫...
  17. J

    MHB What is the method for integrating 1/(1+x^n) using roots of polynomials?

    $(1)\displaystyle \;\; \int\frac{1}{1+x^6}dx$ $(2)\displaystyle \;\; \int\frac{1}{1+x^8}dx$
  18. J

    MHB Integral $\displaystyle\int \frac{1}{\sqrt[4]{1-x^4}}dx$ Solution

    $\displaystyle \int\frac{1}{\sqrt[4]{1-x^4}}dx$
  19. P

    Help with evaluating indefinite integral

    Homework Statement Evaluate the integral: ∫ {√[(a^2)-(x^2)] / (b-x)} dx Homework Equations ∫ u dv = uv - ∫v du The Attempt at a Solution I've tried using integration by parts but it makes the integral even more complex. I also tried using the table of integrals to find a solution to no...
  20. F

    Question about Indefinite integrals

    Homework Statement I hope this is in the right forum, because this is a question on theory and not related to a specific problem. I was reading onlne about the Fundamental Theorem of Calculus. On one site the author wrote: F(x) = \int_{0}^{x} f(t) dt Later, he wrote: \int_{a}^{b}...
  21. T

    Finding Indefinite Integral of a combination of hyperbolic functions

    Homework Statement Compute the following: \int \frac{cosh(x)}{cosh^2(x) - 1}\,dx Homework Equations \int cosh(x)\,dx = sinh(x) + C The Attempt at a Solution I had no clue where to start, so I went to WolfRamAlpha, and it used substitution but it made u = tanh(\frac{x}{2})...
  22. T

    Calculating Constants in indefinite integral with 2 values for f.

    Homework Statement Find the function f(x) such that f''(x) = \frac{1}{x^2}, f(1) = 0 and f(e) = 0 Homework Equations \int f''(x)\,dx = f'(x) + c \int f'(x)\,dx = f(x) + cx + C The Attempt at a Solution f''(x)= \frac{1}{x^2} f'(x)= \int \frac{1}{x^2}\,dx = \frac{-1}{x} + c f(x) = -\int...
  23. Saitama

    Solving the Indefinite Integration Problem

    Homework Statement The value of \int_0^{1} (\prod_{r=1}^{n} (x+r))(\sum_{k=1}^{n} \frac{1}{x+k}) dx equals: a)n b)n! c)(n+1)! d)n.n! (Can someone tell me how to make bigger parentheses using latex?) Homework Equations The Attempt at a Solution I know that the question becomes...
  24. C

    Indefinite Integration of a Rational Expression

    Homework Statement <Indefinite integral sign here>[r^2 -2r] / [r^3 - 3r^2 + 1]dr or the second example in the "Substitution" section here: http://people.clarkson.edu/~sfulton/ma132/parfrac.pdf Homework Equations nada. The Attempt at a Solution Nothing to really attempt, I just...
  25. N

    Indefinite Integration of function's like log(cos(x))?

    Indefinite Integration of function's like log(cos(x))? Can anyone please help me to calculate Indefinite Integration of function's like log(cos(x))?.
  26. C

    Indefinite integral with a rational function

    EDIT: Problem found. This thread can now be ignored.Homework Statement Find the indefinite integral. Homework Equations ((y^2-1)/y)^2 dy The Attempt at a Solution I've attempted a few things. I first attempted to split the statement inside the outer parentheses into two fractions; (y^2/y...
  27. N

    Indefinite integration substitutions: 'any' permissible?

    Hello! Permissible is probably the wrong word, but here's what I am having difficulty with: With substitutions in integration to make the integral easier to solve, there doesn't seem to be a restriction on the substitution one can use with indefinite integration. If one function, or part...
  28. S

    Indefinite Integral for -.5*(ln(2))^2

    Hello, I have recently encountered an integral that I have been able to evaluate in a sick, unholy way, and for making a proof much more elegant I would like a simple way to evaluate the integral from 0 to infinity of ln(x)/(e^x+1) . thank you!
  29. L

    How to solve these indefinite integrals of composite functions

    Homework Statement Well I have these three different integrals: \int{\frac{1}{\sqrt{4x^2-1}}dx} \int{\frac{1}{4-x^2}dx} \int{\frac{1}{x^2+4x+8}dx}Homework Equations Yeah well not exactly sure how to approach this... Do you use integration by substitution, where you come up with some...
  30. L

    Need help solving this indefinite integral via integration by substitution

    Homework Statement Calculate the following integral: \int{\frac{\sqrt{x+1}}{x+5}dx} \ , x ≥ 1 By using the following substitution: t=\sqrt{x+1} Homework Equations Well using the integration by substitution formula. The Attempt at a Solution So I have t=\sqrt{x+1}...
  31. B

    Indefinite Integration: Explaining the Point Behind It

    Presently, I am reading about computing definite integrals; and in one of the examples the authors provides, there is a statement made: "Recall that the point behind indefinite integration...is to determine what function we differentiated to get the integrand." I was wondering if someone...
  32. D

    Indefinite Integration of 1/(3√x^2): Solving for x

    Homework Statement 1 / (3√x2 ) Homework Equations The Attempt at a Solution the overall power of x in denom becomes ( 1/2 * 2 * 1/3 = 1/3) taking in num , it becomes (-1/3 + 1 = 2/3) so answer should be x2/3 / (2/3) which is wrong , please help
  33. P

    Bringing limit under indefinite integral

    Homework Statement Given:lim_{n\rightarrow ∞} \int^{a^n}_{1} \frac{t^{1/n}}{(1+t)t} dt=\int^{∞}_{1} \frac{1}{(1+t)t} dt a - Natural number. I need to prove that I can bring limit under the integral sign. Homework Equations The Attempt at a Solution I've got this so far: | \int^{a^n}_{1}...
  34. C

    Finding the Indefinite Integral Extension Questions

    Homework Statement ∫8x3e-cos(x4+4)sin(x4+4)dx Homework Equations Let u = cos(x4+4) The Attempt at a Solution I know the answer does not have the sin in it and only the e remains, because when the integral is found e stays unchanged. I could find somewhere online to calculate it...
  35. T

    Solve ∫(tanxsec^{2}x)dx Integral with Substitutions

    ∫(tanxsec^{2}x)dx <---Original function to integrate. I do: ∫(tanxsec^{2}x)dx ---> ∫(tanx\frac{1}{cos^{2}x})dx ---> ∫((\frac{sinx}{cosx})(\frac{1}{cos^{2}x}))dx ---> ∫(\frac{sinx}{cos^{3}x})dx ---> substitution: [t=cosx , dt=-sinxdx -> [itex]\frac{dt}{-sinx}[/itex]=dx] --->...
  36. T

    Indefinite integrals. Arriving at different results.

    *SOLVED* Indefinite integrals. Arriving at different results. Mistake found. Thanks!, everything looks correct now.
  37. J

    MHB What Is the Indefinite Integral of \( \frac{e^x}{1+x} \)?

    $\displaystyle \int \frac{e^x}{1+x}dx$
  38. A

    Indefinite integral involving arctan and ln

    Homework Statement ∫ 1/x arctan (lnx) dx Homework Equations The Attempt at a Solution 1.U substitution. SO u = ln x, du= 1/x dx ∫ arctan u du 2.by parts: u = arctan u du = 1/ 1+u^2 v = 1 dv = du 3. uv - ∫vdu = artan u - ∫ 1/ 1+u^2 =...
  39. J

    MHB Indefinite Integral: $\int \frac{1}{\sqrt{\sin 2x}}dx$

    $\displaystyle \int \frac{1}{\sqrt{\sin 2x}}dx$
  40. J

    Find the following indefinite integral

    Homework Statement find the indefinite integral of ∫x√(1-x^2) dx Homework Equations The Attempt at a Solution ∫x√(1-x^2) dx let x = sinθ dx = cosθ dθ now sin^2θ + cos^2θ = 1 => cosθ = √1-sin^2θ ( for the form √(1-x^2)) ∫x√(1-x^2) dx => ∫sinθ (√1-sin^2θ) cosθ dθ =>...
  41. C

    Calculating indefinite integrals

    Homework Statement a) S 13(4^x + 3^x)dx b) S (cosx + sec^2x)dx c) S (3-(1/x))dx d) S e^(7x)dx Homework Equations The S is supposed to be the integration sign The Attempt at a Solution Are these correct or at least close? a) = 13((4^x)/(ln(4) + (3^x)/(ln(3))) + C b) =...
  42. M

    Interpretation of dx as the differential of x for Indefinite Integrals

    Interpretation of "dx" as the differential of x for Indefinite Integrals This question is concept-as-opposed-to-calculation based. I understand that when one sees the integral sign, followed by f(x)dx, that we can think of this as the indefinite integral, or antiderivative of f(x), with...
  43. C

    Indefinite Integral Question; e^x

    Homework Statement Find the indefinite integral (preferably using u-substitution): ∫(ex-e-x)2 dx Homework Equations N/A The Attempt at a Solution To be honest, I'm slightly confused as to which path I'm supposed to take with this, especially since I'm not sure what I should be...
  44. C

    Substitution Method on indefinite integral

    Say we are solving an indefinite integral ∫x√(2x+1) dx. According to the textbook, the solution goes like this. Let u = 2x+1. Then x = (u-1)/2. Since √(2x+1) dx = (1/2)√u du, x√(2x+1) dx = [(u-1)/2] * (1/2)√u du. ∫x√(2x+1) dx = ∫[(u-1)/2] * (1/2)√u du. <= What justifies this?? The...
  45. Square1

    Indefinite forms and l'hopital

    Homework Statement *indeterminate* oops the limit of x^x as x goes to zero from the right Homework Equations Going to be using L'hopital, and related algebraic manipulations to convert to indefinite form 0/0, infinity/infinity The Attempt at a Solution My understanding is that this limit...
  46. C

    Finding the indefinite integral

    Homework Statement \int(x^(1/3)/(x^(1/3)+1))dx Homework Equations I know I have to use u substitution u=x^(1/3) du=1/(3x^(2/3))dx The Attempt at a Solution I know that the denominator of the equation will be u+1, but I don't understand how to find the numerator because I thought...
  47. A

    Calculating indefinite integral

    Homework Statement hey could you help me to calculate the indefinite integral of y=√(x+1)/√(x+2) Homework Equations The Attempt at a Solution tried to set x+1=u and integrate it by substitution but didnt work
  48. S

    Is there such a thing as an indefinite multiple integral?

    A calculus book I am looking at ("Early Transcendentals") does not seem to mention it, but it seems like it is possible, with the constants of integration being functions that have no component in variable being used for the integration. Any insight? Articles?
  49. J

    Solv Indefinite Integral: x^3/sqrt[1 + x^2] dx

    I'm having a problem with the following integral: x^3/sqrt[1 + x^2] dx Can this be done with substitution or integration by parts? Throw me some hints at this one please! Sorry I forgot to include my attempt. I tried solving this by substitution, letting u=1-x^2. Then letting (-1/2)du =...
  50. E

    What is the Indefinite Integral of x*arsinh(x^2)?

    Hi guys, I don't even know where to begin with this question. Find the following indefinite integral: \int x.arsinh (x^2) dx Thanks very much for any help, its much appreciated.
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