What is Indefinite: Definition and 299 Discussions

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. R

    Indefinite Integral of 5*(sin(6x)/sin(3x)) - Help Needed

    Homework Statement The integral of 5*(sin(6x)/sin(3x))dx The Attempt at a Solution I'm not quite sure what to do with this one. I moved 5 to the left of the integral, but then I'm lost. Apparently I'm rusty on these trig identities. Could anyone help me get started? Thank you.
  2. N

    Evaluating Indefinite integrals

    Homework Statement Evaluate \oint x^2 (1-x^3)^6 dx Homework Equations The Attempt at a Solution let u= 1-x^3 du= -3x^2 -1/3 du= x^2 dx -1/3 \oint (u)^6 = -1/3 (u^7/7) = -1/21 (1-x^3)^7 + C Is this done correct? I think I followed all the right steps but there is...
  3. P

    Indefinite integral and Fundalmental of calculus?

    Homework Statement What is the connection between the Indefinite integral and the Fundalmental theorem of calculus (1st part)? The Attempt at a Solution They are the same to me but the FT is more formal.
  4. J

    Indefinite Integrals: How Were They Figured Out?

    I've been wondering how all those indefinite integrals in a comprehensive table were figured out. Can they all be done with one (or some combination) of the standard methods, (substitution, parts etc.)? Or did somebody just poke around until they figured them out? For example, how do you find...
  5. U

    Mastering Indefinite Integrals: Tips and Tricks for Evaluating Tricky Functions

    How can I evaluate \int\frac{dx}{\sqrt{1-2x-x^2}} using inverse trig functions? Thanks.
  6. U

    Another indefinite integral question?

    How to evaluate \int{\frac{\arccos{x}}{x^2}\,dx}?
  7. U

    Mastering Integration by Parts: Proving the Indefinite Integral Formula

    Hi, I need help evaluating the following integral by integration by parts: \int(a^2-x^2)^n\,dx. Specifically I am supposed to prove the following formula: \int(a^2-x^2)^n\,dx=\frac{x(a^2-x^2)^n}{2n+1}+\frac{2a^2n}{2n+1}\int(a^2-x^2)^{n-1}\,dx+C Any hints would be appreciated. Also, does...
  8. Y

    How to evaluate an indefinite integral

    how to evaluate the indefinite integral \int \frac{1}{\sqrt{x^2-1}} dx
  9. Y

    How to Evaluate Indefinite Integrals with Radical Expressions?

    how to evaluate the indefinite integral ∫(x^2-1)^(-1/2) dx and ∫x^(-1)*(1-x^2)^(-1/2) dx
  10. R

    Indefinite Integration Problem

    Homework Statement Integrate: \int \frac{1}{\sin{x}+cos{x}}dx Homework Equations The one above and basic integration formulae which need not be mentioned. The Attempt at a Solution \int \frac{1}{(\sin{x}+cos{x})}...
  11. 0

    Don't understand why an indefinite integral is valid only on a interval

    Don't understand why "an indefinite integral is valid only on a interval" Hi I'm using Stewart's Calculus, in the section of indefinite integral, they say: "Recall from Theorem 4.10.1 that the most general antiderivative on a given interval is obtained by adding a constant to a particular...
  12. E

    Solve Int. 1: Find x^7, x^5, x^3 Terms in Answer

    1. \int(x^{2} + 5)^{3}dx This is what the book gives as the answer 1/7x^{7} + 3x^{5} + 25x^{3} + 125x + C I got something way different. Where are they getting the 3x^5 and 25x^3 from? Thanks. -v.b.
  13. R

    Solving Indefinite Integral: F(x)= \int\frac{1}{t}dt from x to 2x

    Homework Statement How is this function continuous from 0 to infinity F(x) = \int\frac{1}{t}dt from x to 2x Homework Equations I am fairly sure that this equation uses the properties of natural logs to solve. Also an infinite function has a derivative that is equal to 0. The...
  14. A

    Indefinite Integrals: Solving Homework Problems

    Homework Statement Hey guys, I'm trying to teach myself how to integrate an indefinite integral. I just am wondering what you can do with something like this: Homework Equations \int 15/(3x+1) dx The Attempt at a Solution I'm trying to figure out how to go backwards, but I...
  15. A

    Complete ALGO to solve a indefinite integral ( classroom questions )

    Helo everyone, can somebody post the best algorithm/strategy to solve indefinite integral questions which are usually asked to undergraduates. The most general set of steps that can be applied to every question one encounters in the classroom. Algo that though may be proved to be inconvenient...
  16. A

    Verifying Integrals and Solving for Unknown Functions

    Homework Statement Evaluate the Integrals: \int \frac{-2}{\sqrt{1 - x^2}} dx \int \frac{2x+5}{x^2+6x-3} dx \int \frac{x^3}{x^2-1} dx \int \frac{x}{1+x^4} dxVerify that this integral is correct: \int ue^a^u du = \frac{e^a^u}{a}(u-\frac{1}{a})+C
  17. A

    Integrate x^3/(x^5-1): Solutions

    Hi, here is the question integrate x^3/(x^5-1)
  18. O

    I on this indefinite integral

    Homework Statement ok I am given this problem indef. int (1+tan^2*5x)dx i need to use the u subsitution method to find the answer but i cannot seem to find what to subsitute the worksheet says the answer is " one-fifth*tan5x+C Homework Equations The Attempt at a Solution
  19. B

    Solving Indefinite Integral: $\int \frac{sec^2 x}{\sqrt{1-tan^2 x}}dx$

    Homework Statement Find the indefinite integral of \int \frac{sec^2 x}{\sqrt{1-tan^2 x}} dx I'm stuck on how to proceed with the denominator. I know that \sqrt{1+tan^2 x} is equivalent to \\sec\theta but I can't seen to find an equivalent to what I have. Can anyone give...
  20. E

    Indefinite Integrals / Laplace Transforms

    Homework Statement Using improper integrals, find the Laplace transform of f(t)=t, determining the values of s for which the transform is valid.Homework Equations The Laplace transform F(s) of a function f is defined as ∞ / F(s)= | f(t)e^(-st) dt...
  21. C

    How Do I Solve the Integral of cos(x)sin(x)dx?

    Problem: [int]cosx(sinx)dx Given: x=pi; f(pi)=13.4 I am utterly confused on how to solve this integral. I am 99% positive (which is nothing in the math world) that I need to apply the product rule to all of this in order to find the antiderivative. However, no matter how I think of going about...
  22. W

    Indefinite Integration by u-sub/trig sub

    Homework Statement Integrate (x^3)sqrt(1-x^2) Homework Equations The Attempt at a Solution I used trig. substitution along with u substitution and came up with (x^4)/4 +C which I know is wrong. My professor gave the answer -(((3x^2)+2)((1-x^2)^(3/2)))/15 . Please help!
  23. F

    Indefinite Integration Derivation ?

    Homework Statement I want to prove the standard result for indefinite integrals that \int \frac{1}{a^2-x^2} .dx\ =\ \frac{1}{2a}\ln{(\frac{a+x}{a-x})} \\ \mbox{But the problem is that i am unable to do so. I get this--} \int {\frac{1}{a^2-x^2} .dx } \\ = \frac{1}{2a}\int...
  24. I

    Can the Chain Rule Be Applied in Reverse for Integrating Functions Like u^n?

    There is a simple formula for calculating \frac{df(x)}{dx} u^n where u is a function of x and n is a positive rational number: \frac{df(x)}{dx} u^n = nu^{n-1} \ast \frac{du}{dx} . Is there a similar formula for calculating \int u^n dx where u is a function of x and n is a positive rational...
  25. J

    Calculate Effective Annual Rate for 6% Compounding Indefinitely

    periods. Like (1+6%/100)^100-1=0.061817441 (1+6%/1000)^1000-1=0.061834635 does it converge to a limit of like 0.06184 or something like that?
  26. quasar987

    Change of variable in indefinite integrals

    I've had this very basic question on the back of my mind for 2 almost years now and I think I've found a satisfactory answer. The question is this most simple one: how do we justify a change of variables such as \int e^{ax}dx = \int \frac{1}{a}e^udu in an indefinite integral? My "solution" is...
  27. S

    Evaluating an Indefinite Integral of cos^4(x)sin(x)dx

    evaluate the indefinite integral cos^4(x)sin(x)dx I tried using the half angle formula but this gives me a much more difficult integral, so i resorted to just regular substitution but am not sure if I can do this. u = cos(x) du = -sin(x)dx indefinite integral -u^4du then -1/5(u)^5...
  28. D

    Evaluating Indefinite Integrals for Dan

    Hey. Say i was given this indefinite integral to evaluate: http://img126.imageshack.us/img126/6374/aaaaog3.gif How could i do that? I can do it by first expanding it all, but that takes a very long time and is quite tedious, especially with such a large index as 7. Is there another way i...
  29. G

    How Do You Integrate (e^ax)cos^2(2bx)dx Correctly?

    I'm supposed to integrate the following expression, and supposedly there is a very simple way to do so. Maple comes up with something rediculous, so I'd appreciate any input. Sorry about the short hand, don't know how to make everything pretty on here: Integral[(e^ax)cos^2(2bx)dx] where a and...
  30. S

    Indefinite integral substitution

    evaluate the indefinite integral ((e^x)/((e^x)+1))dx I let u = ((e^x)+1) then du = (e^x)dx which occurs in the original equation so.. indefinite ingegral ((u^-1)du) taking the antiderivative I get 1 + C is this right? thanks!
  31. U

    Do quantifiable values become less definite as they increase?

    i have a small (i think) question: a value of zero is a definite value, right? it's easily quantifiable. you either have it or you don't. and a value of 1 is also definite. however, a value of infinity is not definite. it's an indefinite value. now, the question is... do quantifiable...
  32. C

    Indefinite integral of sin^4xdx

    Hi everyone. I'm having some trouble evaluating the following integral \int{sin^4xdx} First let me start off by showing what I did. = \int{(sin^2x)(sin^2x)dx} =\int{[\frac{1}{2}-\frac{1}{2}cos(2x)] \ [\frac{1}{2}-\frac{1}{2}cos(2x)]dx...
  33. N

    Integrate this indefinite integral: 1/(x-6)^2 dx

    I need to integrate this indefinite integral: 1/(x-6)^2 dx Here is my work... Let u= x-6 du/dx=1 so: integral 1/u^2 du = 3/u^3 + c (constant) =3/(x-6)^3 + c Have I gone wrong? And if so where? Thanks
  34. A

    Solving Indefinite Integrals: "int (1/(sqrt -x^2 -2x))dx

    I have: int (1/(sqrt -x^2 -2x))dx so I rewrite (-x^2-2x) --> 1-(x+1)^2 and swap those two. then I say t=x+1, and substitute that in. So now I have: int (1/(sqrt 1-t^2)) dt Here I get stuck, can anyone please help?
  35. D

    Evaluating indefinite integral - toughie

    Evaluating indefinite integral -- toughie! I have the velocity function v(x) = [(k*x^2)/(2*m)] + v0 I need to integrate this to get position as a function of time. So v = dx/dt. Separating variables, I get t = Integral [2m/(2mv0 + kx^2)] Here's where I'm stuck...If i pull out the 2m, then I...
  36. O

    Indefinite Integration Problem

    Calc I - Simple Indefinite Integration Problem Hello, Here is an indefinite integration problem I have been working on. Would anyone be willing to check my solution? Are my assumptions about replacing the C and -C correct? http://img457.imageshack.us/img457/8933/problem0kw.jpg"...
  37. Orion1

    Indefinite Integration Problem

    How is this problem integrated? \int \sqrt{ \sin x} \; dx
  38. C

    Find Indefinite Integral of 1/[(e^x)+(e^-x)]

    How do I find the indefinite integral of 1/[(e^x)+(e^-x)] ? Do I have to multiply by [(e^x)-(e^-x)]/[(e^x)-(e^-x)] to eliminate the denominator? !
  39. cepheid

    What is the True Definition of Indefinite Integrals?

    Well, this is an embarrassingly elementary question, but in my lecture slides (for an electrical engineering course, not a math course) the prof suddenly springs this claim on us: The true definition of an indefinite integral is: \int{f(t)dt} \equiv \int_{-\infty}^{t} {f(\tau) d\tau}...
  40. H

    Integrate x^2/Sqrt[1 - x^2] - Solve 0=0

    \!\(∫x^2/Sqrt[1 - x^2] \[DifferentialD]x\) I need to find the integral of (x^2)/ Sqrt(1-(x^2)) if the above doesn't work properly integration by parts results in 0=0 how do i do this?
  41. L

    How do you find the indefinite integral of xsinx

    I am just curious I was thinking about this and if anyone could explain I would appreciate it. I am curious to know how to find the indefinite integral of xsinx with respect to x. Thanks, David
  42. P

    Solving Int. sin(9x)sin(16x)dx w/o Multiple Angles

    \int sin(9x)sin(16x)dx is there another way of solving the problem above besides using the multiple angles formula?
  43. C

    How Do You Set Up Indefinite Integrals for Different Functions?

    Hello all If you have the funtions: y = x^2, y = sin x, y = 2x^4 and you are asked to set up the corresponding integrations, would it be: \int^b_a 2u du = x^3 \int^b_a -\cos u du = \sin x \int^b_a 8u^3 du = 2x^4 Thanks
  44. H

    From indefinite integral to fundamental theorem of calculus, how does it all link?

    Hi there, Can someone explain to me what the following are and how each one is used as a tool for the next one: 1)Indefinite integral 2)Riemann Sum 3)Definite Integral 4)Fundamental Theorem of Calculus(The part which says that the derivative of the integral of f(t)dt from a to x is...
  45. Q

    Definite and Indefinite intregrals.

    Ok. Im' confused between the difference of definite and indefinite integrals. \int\limits_a_b \int The first integral here which is \int\limits_a_b is about area below a curve. Where a and b is the difference of the area under the function f(x). The \int\ is just the...
  46. E

    Solving Indefinite Integral of Normal Equation

    I've been trying to integrate the following function but have gotten somewhat stuck doing it. The answer i managed to produce gave some bogan answers. the integral in question is \int e^\frac{-(x-\mu)^2}{(2\sigma)^2} where \mu and \sigma are constants. its part of the normal...
  47. C

    Should You Use Indefinite Integrals for Deriving Formulas of 1/(x+1)?

    When they ask you to set up integral formulas for the derivative of 1/(x+1), would you use the fundamental theorem of calculus and set up a definite integral, or an indefinite integral. Can someone help me clarify this? Thanks
  48. D

    What is the Correct Indefinite Integral for cos(5x) + cos(4x) / (1-xcos(3x))?

    Hi! I am stuck with this integration problem: Thanks in advance.
  49. C

    Evaluate the indefinite integral.

    \int sin(7x)sin(13x)dx i just need to know how to start this, i can't use u-du... i can't borrow anything... so how would i start this?
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