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. chwala

    Find the indefinite integral of the given problem

    Now the steps to solution are clear to me...My interest is on the constant that was factored out i.e ##\frac{2}{\sqrt 3}##... the steps that were followed are; They multiplied each term by ##\dfrac{2}{\sqrt 3}## to realize, ##\dfrac{2}{\sqrt 3}\int \dfrac{dx}{\left[\dfrac{2}{\sqrt...
  2. M

    Indefinite Integration of Heaviside function muliplied by a function

    Will it be [{(r-a)/r}*H(r-a)]
  3. E

    MHB Indefinite integral in division form

    I have the following integration - $$\int \frac{2}{x - b \frac{x^{m - n + 1}}{(-x + 1)^m}} \, dx $$ To solve this I did the following - $$\int \frac{1 - b \frac{x^{m - n}}{(-x + 1)^m}+1 + b \frac{x^{m - n}}{(-x + 1)^m}}{x(1 - b \frac{x^{m - n}}{(-x + 1)^m})} \, dx $$ Which gives me -...
  4. Istiak

    How to find the constant in this indefinite integration?

    $$x(t)=\int \dot{x}(t)\mathrm dt=vt+c$$ That's what I did. But, book says $$x(t)=\int \dot{x}(t)\mathrm dt=x_0+v_0 t+ \frac{F_0}{2m}t^2$$ Seems like, $$x_0 + \dfrac{a_0}{2}t^2$$ is constant. How to find constant is equal to what?
  5. A

    I What is the indefinite integral of Bessel function of 1 order (first k

    Hi When we find integrals of Bessel function we use recurrence relations. But this requires that we have the variable X raised to some power and multiplied with the function . But how about when we have Bessel function of first order and without multiplication? How should we integrate it ?
  6. greg_rack

    Problem solving a parametric indefinite integral

    Since ##h## and ##k## are constants: $$\frac{h}{k}\cdot \int \frac{1}{y(h-y)} \ dy$$ Now, rewriting the integrating function in terms of coefficients ##A## and ##B##: $$\frac{1}{y(h-y)}=\frac{A}{y}+\frac{B}{h-y}\rightarrow B=A=\frac{1}{h} \rightarrow$$ $$\frac{1}{h}\int \frac{1}{y}\ dy +...
  7. greg_rack

    Apparently impossible indefinite integral?

    Hi guys, I got to solve this integral in a recent test, and literally I had no idea of where to start. I thought about substituting ##tan(\frac{x}{2})=t## in order to apply trigonometry parametric equations, integrating by parts, substituting, but I always found out I was just running in a...
  8. greg_rack

    Solving an immediate indefinite integral of a composite function

    That's my attempt: $$\int (\frac{1}{cos^2x\cdot tan^3x})dx = \int (\frac{1}{cos^2x}\cdot tan^{-3}x) dx$$ Now, being ##\frac{1}{cos^2x}## the derivative of ##tanx##, the integral gets: $$-\frac{1}{2tan^2x}+c$$ But there is something wrong... what?
  9. agnimusayoti

    Indefinite integral of cross product of 2 function

    I've tried with this work in attachment. i&m not sure of my answer is correct.
  10. C

    Can indefinite integration be simplified using substitution?

    Let x=t^2 Then dx=2t dt Integral of 1/(x(1-x))^(1/2)dx = integral of 2tdt/t(1-t^2) ^(1/2) = integral of 2dt/(1-t^2) ^(1/2) = 2 arcsin(t) +c = 2 arcsin(rt(x)) +c. But the answer in my book is arcsin(2x-1) +c. Tell me how 2 arcsin(rt(x) +C= arcsin(2x-1) +c I know the constant will vary for both...
  11. E

    Definite and indefinite integration in the definition of work

    This is going to sound like a silly question, but here we go anyway! I've always thought about a definite integral being used for modelling a change in some quantity whilst an indefinite integral is employed to find the defining function of that quantity. For example, consider the...
  12. Michael Santos

    The indefinite integral and its "argument"

    Homework Statement The indefinite integral $$\int \, $$ and it's argument. The indefinite integral has a function of e.g ## \cos (x^2) \ ## or ## \ e^{tan (x)} \ ## If the argument of ## \cos (x^2) \ ## is ## \ x^2 \ ## then the argument of ## \ e^{tan(x)} \ ## is ## \ x \ ## or ## \ tan (x) \...
  13. M

    MHB Find Velocity of Particles: Indefinite Integrals

    To help find the velocity of particles requires the evaluation of the indefinite integral of the acceleration function, a(t), i.e. v = Z a(t) dt. Your help greatly appreciated.
  14. D

    I Is there a way to find the indefinite integral of e^(-x^2) or e^(x^2)?

    I was wandering if there is a way to understand whether it is possible to find an indefinite integral of a function. Let's say e^(-x^2) or e^(x^2)... They can't have indefinite integrals, but how can I say it? Is there a theorem or something?
  15. nightingale123

    Finding an indefinite integral

    Homework Statement Calculate the indefinite integral of the function ## \int\frac{3x^3}{\sqrt{1-x^2}}## my book gives the answer ##-(2+x^2)\sqrt{1-x^2}+C## Homework EquationsThe Attempt at a Solution So I started trying to calculate this indefinite integral by using a substitution...
  16. J

    MHB Indefinite integration involving exponential and rational function

    Calculation of $\displaystyle \int e^x \cdot \frac{x^3-x+2}{(x^2+1)^2}dx$
  17. A

    I Integral of the momentum (with respect to time)

    Hi everybody ! Can anyone help me with this problem: Which is the (indefinite) integral with respect to time of the momentum of a particle of rest mass ##m_0##? ##\int \dfrac{m_0\;\mathbf{v}}{{\sqrt{1-\dfrac{\mathbf{v}\cdot\mathbf{v}}{c^2}}}}\;dt## where ##m_0## is invariant with respect to...
  18. J

    I Question about definite and indefinite integrals

    First, just to check, I write what I think and let me know if I am wrong: The definite integral of a function gives us a number whose geometric meaning is the area under the curve between two limiting points. We can calculate this integral as the limit of the sum of the rectangles and the...
  19. NickTesla

    B How Do You Simplify 12/4 in an Indefinite Integral?

    doubt in this fraction in here Because he, simplify 12 with 4 ?? do not understand! someone could make another example ,with fraction ! Thank you!
  20. G

    Need help with this indefinite integral question please.

    Homework Statement find the following integral: cos(x/2) - sin(3x/2) dxHomework Equations I think the substitution method has to be used. Solve integrals by parts. The Attempt at a Solution Let u = x/2 cosu du/dx=1/2, I then inverted it so dx/du = 2/1 = 2 So dx=2du Now I have cosu2du Do I...
  21. Valour549

    I Is this a Definite or Indefinite Integral?

    F(x) = \int_a^x f(t) dt I have found various arguments online for both. Personally I think it's an indefinite integral because: 1) Its upper limit is a variable and not a constant, meaning the value of the integral actually varies with x. This is no different to the family of primitives...
  22. K

    Determine the indefinite integral

    Hello, Please can someone help me solve my problem. I have recently submitted my answer and had my work referred for an error. I have pictures of my question and working out, however i can not seem to post them on the page. can i email them to someone for advice/guidance Thanks
  23. petrushkagoogol

    Recursion: Avoiding Stack Overflow Errors

    Upto how many levels of recursion can be used in an algorithm to avoid stack overflow error ?
  24. micromass

    Insights Some Misconceptions about Indefinite Integrals - Comments

    micromass submitted a new PF Insights post Some Misconceptions on Indefinite Integrals Continue reading the Original PF Insights Post.
  25. Saracen Rue

    B Making a definite integral equal and indefinite integral?

    I have a calculator which allows me to sketch indefinite integrals - it assumes c = 0. However, when I try to use Desmos Online Graphing Calculator, it won't let me do this with it's integral function. It keeps trying to make me use definite integrals. I know that ∫(a,b,f(x)dx = F(a) - F(b), so...
  26. P

    MHB Kishan's question via email about an indefinite integral

    What is the $\displaystyle \begin{align*} \int{ \frac{54\,t - 12}{\left( t- 9 \right) \left( t^2 - 2 \right) } \,\mathrm{d}t } \end{align*}$ We should use Partial Fractions to simplify the integrand. The denominator can be factorised further as $\displaystyle \begin{align*} \int{ \frac{54\,t -...
  27. P

    MHB Effie's question via email about an indefinite integral.

    What is the indefinite integral (with respect to t) of $\displaystyle \begin{align*} 50\,t\cos{ \left( 5\,t^2 \right) } \end{align*}$? $\displaystyle \begin{align*} \int{ 50\,t\cos{\left( 5\,t^2 \right) } \,\mathrm{d}t } &= 5\int{ 10\,t\cos{ \left( 5\,t^2 \right) }\,\mathrm{d}t } \end{align*}$...
  28. B

    I Does X times 0 always equal 0 or are there exceptions?

    Not sure if the correct term is indefinite or undefined... I mean something like an infinite series that does not sum to a particular value, like this: X = 1 - 1 + 1 - 1 + 1 - 1 + 1... where pending the placement of parentheses one can infer multiple answers for X So, is it proper to say X...
  29. T

    Solve Indefinite Integral: U Substitution

    Homework Statement Im looking over the notes in my lecture and the prof wrote, \int_{0}^{2} \pi(4x^2-x^4)dx=\frac{64\pi}{15} Im wondering what's the indefinite integral of this equation. Homework Equations using u substitution The Attempt at a Solution \int \pi(4x^2-x^4)dx= \pi \int...
  30. G

    Finding the indefinite integral of sin^2(pi*x) cos^5(pi*x)

    Homework Statement ∫(sin2(πx)*cos5(πx))dx. Homework Equations Just the above. The Attempt at a Solution I have no idea how pi effects the answer, so I basically solved ∫(sin2(x)^cos5(x))dx. ∫(sin2(x)*cos4(x)*cos(x))dx ∫sin2(x)*(1-sin2(x))2*cos(x))dx U-substitution u = sin x du =...
  31. I

    Indefinite Trignometric Integral

    Homework Statement ∫sinxcos(x/2)dx This isn't an actual homework problem, but one I found that I'm working on for test prep. Homework EquationsThe Attempt at a Solution [/B] ∫sinxcos(x/2) dx = ∫sinx√((1+cosx)/2) dx u = ½ + ½ cosx -2 du = sinx dx -2∫√(u) du = -2(2/3⋅u3/2) + c -2(2/3⋅u3/2)...
  32. Anton Alice

    Fermat's principle seems indefinite

    Hello forum, please take a look at the following picture: It's a salt solution, with increasing refractive index, as you go down the solution. How can I explain this with Fermat's principle? Let's set the starting point A to the point, where the laser beam penetrates the left wall of the...
  33. I

    Calculate indefinite integral using Fourier transform

    Homework Statement Use the Fourier transform to compute \int_{-\infty}^\infty \frac{(x^2+2)^2}{(x^4+4)^2}dx Homework Equations The Plancherel Theorem ##||f||^2=\frac{1}{2\pi}||\hat f ||^2## for all ##f \in L^2##. We also have a table with the Fourier transform of some function, the ones of...
  34. SteliosVas

    Indefinite integral and proving convergence

    Homework Statement okay so the equation goes: ∫(x*sin2(x))/(x3-1) over the terminals: b= ∞ and a = 2 Homework Equations Various rules applying to the convergence or divergence of integrals such as the p-test, ratio test, squeeze test etc The Attempt at a Solution Okay so I have tried...
  35. Chip

    Solving the Indefinite Integral for <xp>=<px>*

    First of all, I'm new here, so please bear with me if the answer to my question can be found elsewhere, but I have been working a problem and searching for an answer for two weeks now without a complete solution. In Eisberg and Resnick chapter 5, problem 15, an essential part of the problem is...
  36. I

    MHB Struggling with a trig indefinite integration

    So here is the problem: Find the anti-derivative of sec 3x(sec(3x) + tan(3x)) Now I have tried foiling it out, and I am stuck at the part where I need to anti-derive Sec(3x)Tan(3x). Any help/tips would be greatly appreciated.
  37. Drakkith

    Evaluating an Indefinite Integral using Substitution

    Homework Statement Evaluate the Integral: ∫sin2x dx/(1+cos2x) Homework EquationsThe Attempt at a Solution I first broke the numerator up: ∫2sinxcosx dx /(1+cos2x) 2∫sinxcosx dx /(1+cos2x) Then I let u = cosx so that du = -sinx dx -2∫u du/(1+u2) And now I'm stuck. I thought about turning...
  38. S

    Finding the Indefinite Integral: Can Multiplying a Constant Change the Solution?

    I have posted my attempt and the problem above. Please help! Thanks in advance!
  39. P

    Indefinite integral with discontinuous integrand

    Suppose ##f## is defined as follows: ##f(x) = 1## for all ##x ≠ 1##, ##f(1) = 10##. Is the indefinite integral (or the most general antiderivative) of ##f## defined at ##x = 1##? I'm asking this question because I already know how to deal with, say, ##\int_0^2 f##; ##f## has only one removable...
  40. Physics-UG

    Indefinite Integral with integration by parts

    Homework Statement Evaluate ∫e-θcos2θ dθ Homework Equations Integration by parts formula ∫udv = uv -∫vdu The Attempt at a Solution So in calc II we just started integration by parts and I'm doing one of the assignment problems. I know I need to do the integration by parts twice, but I've hit...
  41. PWiz

    Indefinite integral of arcsec(x)

    Just for fun, I tried this rather trivial problem, but I think I went wrong somewhere: $$\int arcsec(x) \ dx$$ Let ##arcsec(x)=y## . Then ##x=sec \ y##, or ##y=arccos(\frac 1{x})## So the problem becomes $$\int arccos(\frac 1 {x}) \ dx$$ Let ##\frac 1 {x} = cos \ u## , so that ##dx = secu \ tanu...
  42. B

    Indefinite Integral: How to Use Trig Substitution?

    Homework Statement Find the indefnite integral using trig substitution. ∫[(x^2) / (1+x^2)]dx Homework Equations --- The Attempt at a Solution
  43. S

    What Substitution Solves This Integral?

    1. http://www.imageurlhost.com/images/cnj1t05jh6e4fxqy4i5_integral.png I know that this integral is solved by the sustitution method The Attempt at a Solution I tried converting the integral to the form of Arctanx, but that x2 on the numerator ruined everything. Thanks
  44. Emmanuel_Euler

    Indefinite and definite integral of e^sin(x) dx

    Look to this indefinite integral →∫e^(sin(x))dx Antiderivative or integral could not be found.and impossible to solve. Look to this definite integral ∫e^(sin(x))dx (Upper bound is π and Lower bound is zero)=?? my question is : can we find any solution for this integral (definite integral) ??
  45. karush

    MHB Indefinite integral using trig substitutions

    $\int\frac{1}{\sqrt{2+3y^2}}dy$ $u=\sqrt{3/2}\tan\left({\theta}\right)$ I continued but it went south..
  46. TheDemx27

    Indefinite Integral in Programming

    I've been contributing to an open source calculator, and I wanted a way to take integrals of functions. I suppose you could implement a definite integral function by using Riemann Sums, but I can't find any way to implement indefinite integrals (or derivatives for that matter). I've heard that...
  47. G

    Levi-Civita Symbol and indefinite metrics

    Let ##(M,g)## be an ##n##-dimensional pseudo-Riemannian manifold of signature ##(n_+, n_-)## and define the Levi-Civita symbol via $$\varepsilon_{i_1 \dots i_n} \, \theta^{i_1 \dots i_n} = n! \, \theta^{[1 \dots n]} = \theta^1 \wedge \dots \wedge \theta^n$$ where ##\theta^1, \dots, \theta^n##...
  48. J

    MHB How can we evaluate this indefinite integral of a definite integral?

    Evaluation of Indefinite Integral $\displaystyle \int_{0}^{1} \sqrt{1-2\sqrt{x-x^2}}dx$ $\bf{My\; Try::}$ We can write the given Integral as $\displaystyle \int_{0}^{1}\sqrt{\left(\sqrt{x}\right)^2+\left(\sqrt{1-x}\right)^2-2\sqrt{x}\cdot \sqrt{1-x}}dx$ So Integral Convert into...
  49. karush

    MHB Indefinite integral complete square

    $$\int_{}^{} \frac{1}{\sqrt{16+4x-2x^2}}\,dx$$ $$\frac{\sqrt{2}} {2}\int_{}^{} \cos\left(\frac{x-1}{3}\right)\,dx$$ So far ? Not sure
  50. karush

    MHB Evaluating Integral $$\int \frac{e^{2x}}{u} du$$

    $$\int_{}^{} \frac{e^{2x}}{e^{2x}-2}dx. \\u=e^{2x}-2\\du=e^{2x}$$ Now what?
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