Indefinite Definition and 296 Threads

Homework Statement A time-dependent torque given by a + bsin(ct) is applied to an object that's initially stationary but is free to rotate. Here a, b, and c are constants. Find an expression for the object's angular momentum as a function of time, assuming the torque is first applied at t =...

Homework Statement Evaluate the following limits or determine that the limit does not exist. b) lim (x,y)–>(0,0) (1+xy)^(1/xy) Homework Equations The Attempt at a Solution I have a funny feeling this limit might exist. (Then again I get that feeling about every indefinite...

Is it possible to have a tank of water, run electricity through it, collect the hydrogen and oxygen, use it as fuel to heat the same tank of water into steam, use the steam to spin a turbine generating electricity to run through the water once more to create more hydrogen and oxygen to use as...

Hi I have not studied calculus for a while and I am just seeking some clarification on the following two problems I have attempted to solve. PROBLEM 1 dy/dx = y(x^3 - √x) I have separated the variables as follows: Rewrote equation as dy/dx = y(x^3 - x^1/2) Divided both sides by...

Homework Statement \int (\frac{x}{\sqrt{x+8}}) dx The Attempt at a Solution I got to be honest, I don't even really know where to start with this problem. So bear with me as I take a wild stab in the dark. This section was substitution problems, ... \frac{x}{\sqrt{x+8}} = \sqrt{...

Homework Statement Consider the integral, \int _3 ^7 (\frac{3}{x} + 2) dx a) Find the Riemann Sum for this integral using right endpoints and n=4. b) Find the Riemann Sum for this integral using left endpoints and n=4. Homework Equations The sum, \sum^{n = 4} (\frac{3}{x} + 2) The graph...

[SIZE="4"]Homework Statement Evaluate the integral \int \frac{(a-x)^{r/s-1}}{(b-x)^{r/2}}dx Homework Equations given: s>r The Attempt at a Solution I tried using a substitution: let u=b-x so du=-dx this gives: -\int \frac{(a-b+u)^{r/s-1}}{u^{r/2}}du I don't know what...

Homework Statement The problem is divided into two sections: a) does the improper integral: 2ln(x)/x^7 (from 1 to infinity) Converge or diverge? If it converges, to what value? b) Determine whether the series: sigma n=1 to infinity (2ln(n)/n^7) converges or diverges. Homework...

Homework Statement \int (x+1)^2 dx Homework Equations The Attempt at a Solution I am just getting into this, and this is a simple problem, but my book and I took two separate routes. My question, essentially, is does any constant you get just "combine" with the "any constant" C...

Homework Statement A particle is moving with the given data. Find the position of the particle. a(t)=t^{2}-4t+6, s(0)=0, s(1)=20 Homework Equations The Attempt at a Solution a(t)=t^{2}-4t+6, s(0)=0, s(1)=20 v(t)=\int t^{2}-4t+6 dt v(t)=\frac{t^{3}}{3}-2t^{2}+6t+C_{1} Then I suppose I take...

Homework Statement I need help finding the anti-derivatives (indefinite integrals) of the 2 functions below: 1) e^(sqrt(x)) 2) Sqrt(2x - x^2) Homework Equations The Attempt at a Solution I tried forever at these 2 but I can't figure out a way for either of them. Any...

Homework Statement \int \frac{\sqrt{x^4-1}}{x^3}dx Homework Equations The Attempt at a Solution tried substituting x^4 = \sec^2 \theta to get rid of square root but it was of no use because, I got another complex integral \int \frac{\sin^2\theta}{\cos^{\frac{3}{4}}...

Anyone how to integrate this? Integration by parts doesn't get me anywhere, and there isn't a maclaurin series for ln(x). Thanks! (This isn't a homework question, I just was randomly doing integrals)

Homework Statement S=integral symbol S(5x+7)^28 Homework Equations Substitution The Attempt at a Solution let u = 5x+7 du = 5 S u^28 du = (u^29)/29 du = [5(5x+7)^29]/29 is this correct? I'm not sure...

Homework Statement \int{\sqrt{1+e^x}dx} Homework Equations \int{uv'}=uv-\int{u'v} The Attempt at a Solution I rewrote the integrand as \sqrt{1+(e^{x/2})^2} and used the trigonometric substituition e^{x/2}=tan(\theta), which simplified the radical to...

Hey, all. Anyway, browsing the Internet a bit I found this integral: \int \sqrt{1 + \frac{\ln x}{x}}dx as a proposed problem in a compilation of maths problems, as an integral from the MATYC journal. I gave it to Mathematica and WolframAlpha and they weren't able to solve it...

Homework Statement Show that: Lim [1+1/(2x)]^x = sqrt(e) x->-inf 2. Homework Equations /theorums L'Hopitals ruleThe Attempt at a Solution Let y= [1+1/(2x)]^x lny=ln [1+1/(2x)]^x lny= x ln [1+1/(2x)] Then Ln Lim (y)= x->-inf Lim (lny)= x->-inf Lim x ln...

Given an indefinite integral, \int f(x) dx = F(x) + C, I am having some problems in understanding what this indefinite integral "is". The RHS is clearly a function, but what is the LHS? Judging by the equals sign, it should also be a function, but seemingly it isn't because there's no...

I am continuing here the discussion of side issues from another thread, quoting a number of Careful's promotional posts for indefinite spaces, negative probabilities, and other unconventional ideas for a generalized quantum mechanics. (A Nevanlinna space is a vector space equipped with an...

Homework Statement Evaluate the indefinite integral. Homework Equations I tried to use substitution. The Attempt at a Solution I'm not so good with using the LaTex codes...so I attached a file I made in Word. Thanks in advance!

Homework Statement indefinite integral 5\picos\pit Homework Equations The Attempt at a Solution 5\pi int cos\pit Substitution Method 5\pi x sin (1/\pit

Homework Statement (e^-x)/(1+e^-x)dx Homework Equations Integral of e^x function The Attempt at a Solution I am completely lost with the problem, the fact that it is e^-x and not e^x has me stupped as well as the division.

Homework Statement integral 1/(x(sqrt(x^2 - 4))) Homework Equations I don't know if there are any "equations" for integrals... The Attempt at a Solution Int(1/(x(Sqrt(4(x^2 /4)-1) Int(1/(2x(Sqrt((x^2 /4)-1) 1/2 int(1/(x(Sqrt((x /2)^2)-1) U-sub u=x/2 du=1/2 dx 2du= dx...

This question is bugging me if an indefinite integral is of the form F(x) + C stating that F(x) is an antiderivative of f(x) and since the derivative of a constant is 0 the collection of all of the anti derivatives are of the F(x) + C accounting for the fact any constant can be tagged to the...

I arrived at this problem while trying to find the length of a 3D http://en.wikipedia.org/wiki/Cubic_interpolation" . Basically, I'm having to figure out how to integrate ((At4+Bt3+Ct2+Dt+E)1/2)dt A,B,C,D, and E are constants which have to be plugged in after integration, I'm sorry to say...

This is really a full on homework question but it WILL help me to solve my homework... by helping me fully understand the integral. So I am trying to understand exactly what the indefinte integral means? heres my train of thought... if our function F(x) = x2 then its derivative is F'(x)...

Homework Statement \int \frac{cos x}{sin^2(x) - sin(x)-6}2. The attempt at a solution I first tried factoring the denominator. \int \frac{cos x}{(sin(x) -3)(sin(x)+2)} The first thing that came to my mind was Partial Factoring but I don't think it would work in this case.Thanks in advance!

Homework Statement How do I evaluate this? A hint will do.

I am having much trouble with indefinite integrals - i get most of the basic theory behind them but as soon as i am confronted with a larger more complex question i get stuck too easily. These questions are not for my homework, they are just practice for my test. Any hints, tips and general...

Hello, I'm kind of stuck in this problem. I have to express the integral as a power series. the integral of (e^x -1)/x I thought about evaluating it as f(x)=(e^x -1)/x and treating it as a Taylor series is that correct? Could I have any other hints? I would really appreciate it...

I have a third order, non-linear, homogeneous, constant coefficient ODE that I need to solve but have no idea how to do it. To make matters worse, one of the boundary conditions are indefinite. Here's the equation, y''' + y*y'' - y'^2 + 1 = 0 and the BC's y(0) = 0 y'(0) = 0 y'(\infty) =...

Homework Statement integrate lnsqrt(t)/t , dt Homework Equations The Attempt at a Solution This is the most i can come up with. u = lnsqrt(t), so du = 1/(2sqrt(t))dt , so dt = 2du/sqrt(t) Im stuck @ this point

Homework Statement I started the problem, got stuck. Homework Equations The Attempt at a Solution

Homework Statement Please explain how to use the substitution rule in indefinite integrals. I am unable even to start the problem. Homework Equations The Attempt at a Solution

Homework Statement Hi, can you please check the two problems? (I have never done such before) Homework Equations The Attempt at a Solution

Homework Statement Hi! Can anyone check if I got the right answer? The Attempt at a Solution

Homework Statement ∫cos(x)/sin^2(x)*dx Homework Equations The Attempt at a Solution Based off my earlier question, where is my error please. u=sinx du=cosx*dx ∫u^-1*du sin(x)^-1 1/sin(x) + C -or-csc(x) + C Thanks

Homework Statement ∫cos(x)sin^6(x)*dx Homework Equations The Attempt at a Solution u=sin(x) then du should be -cos(x) according to the integral tables? -∫u^6*du = -u^7/7 -sin^7(x)/7+c yet my book and calculator tell me the answer is positive. How?

1/(4+3x^2) ? I'm trying to use this integration formula to solve for this du ---------- a^2+u^2 I know my a would be 2, but what would my u be? I tried u = 3x and du=3dx and du/3=dx but (3x)^2 would be 9x^2

Homework Statement The problem reads(from the 4th edition of Stewart Calculus "Concepts and Contexts" pg. 394 #17): Evaluate the integral. the indefinite integral of dx/x^2*sqrt(4-x^2) so this would read out as "the indefinite integral of dx over x squared times the square root of 4 minus...

\int\frac{4}{-e^{4x-7}} =ln-e^{4x-7}} =-4x+7+C The answer says it is: =\-e^{-4x+7}+C

S x^2(e^((x^3)+1)) I know I have to use integration by parts, and I'm guessing I should find the derivative of e^((x^3)+1), but I really have no idea where to start...

Homework Statement how to solve the integral of x^3 - 3x^2 + 4x -9 / x^2 + 3 dx Homework Equations using long division The Attempt at a Solution x^2 + 3 divided into x^3 - 3x^2 + 4x -9 I am not sure

Homework Statement integral of 1/x^2/3(1+x^1/3) Homework Equations integral of 1/x dx = ln|x| + c The Attempt at a Solution let u= x ^2/3(1+x^1/3)

Homework Statement \int \frac {2+z^{-1}}{z^{2}} dz The Attempt at a Solution Let: u = 2 +z^{-1} du = -z^{-2} dz dz = -z^{2} du so now its \int \frac {u}{z^{2}} (-z^{2}) du \int \frac {(u)(-z^{2})}{z^{2}} du \int (u)(-1) du and then the...

Homework Statement \int \frac {1}{\sqrt{x}(1+\sqrt{x})} dx The Attempt at a Solution So let u = 1 + \sqrt{x} then du = \frac {1}{2}x^{-1/2} dx So dx should be this: dx = 2x^{1/2} du right? So now the Problem looks something like this: \int \frac...

Homework Statement Find: \int \frac {-1}{x^{2}(1+\frac{1}{x})^{2}} dx Homework Equations Same as before: \int f(u)du = F(g(x)) + C The Attempt at a Solution Let u = 1 + \frac {1}{x} then du = -\frac{1}{x^{2}} so \frac {-1}{x^{2}(1+\frac{1}{x})^{2}}...

Homework Statement This is only an example but I do not understand what they are doing... \int (4x+1)^{3} + (4x+1)^{2}+(4x+1) dx Homework Equations \int f(u) du = F(g(x)) + C The Attempt at a Solution Let u = 4x+1 then du = 4 dx and dx = \frac...

nevermind I got it