parts Definition and 817 Threads

Hello all! I have recently started a Parts Cleaning Machine manufacturing business. Most of my clients are Automobile Manufacturers & Ancillaries. The last couple of years have been disastrous for the automobile industry here. So I was looking to broaden my horizon and target the Steel...

From the logarithmic integral representation of the Dilogarithm, $$\text{Li}_2(x)$$, $$|x| \le 1$$, prove the reflection formula for the Dilogarithm. Dilogarithm definition:$$\text{Li}_2(x) = -\int_0^1\frac{\log(1-xt)}{t}\, dt = \sum_{k=1}^{\infty}\frac{x^k}{k^2}$$Dilogarithm reflection...

integral of arctg(x)/sqrt(1-x^2) maybe u = arctg x du = 1 /1+x^2 but x = tg u maybe this is the way isn't it?

integral is exsqrt(x) ok here u = sqrt(x) du = 1/(2sqrt(x)) dv ex= v= ex so exsqrt(x) - integral( 1/2sqrt(x)ex) And I can't continue because i can not get rid of ex?? How must I proceed??

This isn't really a homework question, more just something I noticed while evaluating an integral and was curious about: At this stage, I was able to simplify the expression before solving for the integral algebraically (since the second iteration yielded the original integral the right...

I know its easier to use the substitution method, by I'm trying to see how it'll work for integration by parts. I follow the LIATE method for integration by parts. Now if I take u=cos(x) and dv = sin(x), the answer changes. Can you please explain this to me? Which is the 'right'...

Homework Statement The rotating parts of a motor have a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. When operating the motor is connected at optimum speed , by means of a clutch, to a shaft which has a counter rotation of 600 rev/min. The shaft has a mass of...

Homework Statement A manager must assess the quality of a new batch of 25 components ready for shipping. Rather than assess each component, a sample of 5 is randomly selected and tested. The quality control specification is that if there are 2 or more defectives in the sample, the...

When you have a fraction, how do you know when to use iteration by parts, or use substituion, pick a u, solve for a value of x (like x=u-2) and then plug in those values?

it is integral of xarctg2x u = arctg2x du =1/(1+x2) or 2(arctgx/(1+x2) ?' I am stuck here dv = x v =x2/2

Homework Statement Let f be continuous on an interval I containing 0, and define f1(x) = ∫f(t)dt, f2(x) = ∫f1(t)dt, and in general, fn(x) = ∫fn-1(t)dt for n≥2. Show that fn+1(x) = ∫[(x-t)n/n!]f(t)dt for every n≥0. ALL INTEGRALS DEFINED FROM 0 to x (I can't format :( ) Homework...

Homework Statement Homework Equations N/A The Attempt at a Solution I can't even begin the attempt because I don't know how you could use intergration by parts for this sum in the first place. Can you help me out?

integral ln(x).cos(x) Here I have some clear ideas U = lnx du = 1/x dv = cosx so int de cosx = v = -sinx -sinxlnx -int (sinx)/(x) Ok I think I must integrate again u= sinx du = cosx dv = 1/x v = lnx Again I got -sinxlnx -int (sinx lnx) But I am stuck here and I don't know how to...

Homework Statement I want to integrate \int_{0}^{a} xsin\frac{\pi x}{a}sin\frac{\pi x}{a}dxHomework Equations I have the orthogonality relation: \int_{0}^{a} sin\frac{n\pi x}{a}sin\frac{m\pi x}{a}dx = \begin{cases} \frac{a}{2} &\mbox{if } n = m; \\ 0 & \mbox{otherwise.} \end{cases} and...

i'm trying to integrate this: $$W=\frac{ε}{2}\int{\vec{∇}\cdot\vec{E})Vdτ}$$ where ε is a constant, E= -∇V, τ is a volume element how do i end up with the following via integration by parts? $$W=\frac{ε}{2}[-\int{\vec{E}\cdot(\vec{∇}V)dτ}+\oint{V\vec{E}\cdot d\vec{a}}$$] where the vector a...

Homework Statement Evaluate the integral. Homework Equations \int e^{2x} sin(3x) dx The Attempt at a Solution I began by using integration by parts. u = sin(3x) v = \frac {e^{2x}} {2} du = 3 cos(3x) dv = e^{2x} dx but I get stuck after that because the...

Hi all ! I'm new here :) So I'm facing some confusions here regarding integration by parts. While surfing through the internet to study more about this topic, I've came across two formulas which are used in solving problems related to integration by parts. They are 1. uv - ∫uv'dx 2. uv -...

When a positive charge leaves the positive part if the battery it has maximum electric potential energy then as it moves through a wire with a zero resistance the charge is closer to the negative side of the battery. So, while traveling in a wire in a circuit does it lose electric potential...

What are the Alternative Parts for Transistor (L14F1) Diode (LD271) IC (S20102) While I was surfing the net in the hope of finding a Solution to this, I found a Thread Regarding the same in this Site, It was Very Helpful, But not mention the part name (code) wise, I am a newbie to...

Homework Statement Integrate the following indefinite integrals A:\int e^x (x^2+1) dx B:\int e^x cos(3x+2) dxHomework Equations \int u dv = uv - \int v du The Attempt at a Solution Part A: I have done the following but when I use an integration calculator online its not what I have (although...

Hi PF. This a fact well aware to just about anyone that has had even basic chemistry, but I'm having a hard time coming to an understanding as to why this must be true. So why? Also, if I knew that some box contained, say, a proton and an electron, could I ever know whether or not, inside...

Homework Statement First make a substitution and then use integration by parts to evaluate the integral. ∫x^{7}cos(x^{4})dx Homework Equations Equation for Substitution: ∫f(g(x))g'(x)dx = ∫f(u)du Equation for Integration by Parts: ∫udv = uv - ∫vdu The Attempt at a Solution So...

Homework Statement Use integration by parts to evaluate the integral. ∫5x ln(4x)dx Homework Equations ∫udv = uv - ∫vdu The Attempt at a Solution So here's my solution: But the computer is telling me I'm wrong :( We haven't learned how to integrate lnx yet, so the...

Hello, I am using a very old textbook from 1895, Loney's Trigonometry, which poses the following problem: If the circumference of a circle be divided into 5 parts, which are in A.P., and if the greatest part be 6 times the least, find in radians the magnitudes of the angles that the parts...

Homework Statement The problem is attached in this post. Homework Equations The problem is attached in this post. The Attempt at a Solution I've set up the integral via disk method: π∫(e^√x)^2 dx from 0 to 1 I've done integration by parts by don't know how to integrate the...

I might need to go to a metal shop/fabricator/what have you soon to have work done on a conceptually simple part that has some elements with measurements on the microscopic scale. Think cylinders with a diameter of .2 microns. Lots of them. I would want it done in aluminum. What would be the...

Homework Statement ∫((z^3)(e^z ))dzHomework Equations I just tried u dv - ∫v duThe Attempt at a Solution u = z^3 dv = e^z du = 3z^2 v = e^z = z^3e^z - ∫(3e^z (z^2)) dz I got this far but after that if I try integration by parts again, it gets too confusing.

Homework Statement ∫cosx(lnsinx)dx Homework Equations The Attempt at a Solution u=lnsinx dv=cosxdx du=cosx/sinx dx v=sinx =(lnsinx)(sinx)-∫(sinx)(cosx/sinx)dx =(lnsinx)(sinx)-(sinx)+C I thought that I did this correctly, but my teacher said that u should...

how do i integrate (xe^(2x))/((1+2x)^2)?? do i substitute 1 + 2x = w? but if i do, how do i proceed from there?

Hey pf! I think this is the correct thread. Basically, if I take a line segment and remove half of it, what happens to the point that is in the middle? Also, what happens if I take a segment [0,1] and take [0,1/2) versus [0,1/2]? What length do I have remaining for each of these? Thanks!

How would you integrate this: ## \int x df(x) ## In general, how is this solved: ## \int 1df(x) ## Can you use integration by parts? I tried, but kept getting 0 since I let ## 1 = u## but then ##du = 0## for later purposes. Also, if ## df(x) = u ## then I am still stumped on how to take the...

is this a drum brake ? there are a piece of metal sheet assemble to this thing, and what's is the name of the metal?

Homework Statement Find the real and Imaginary parts of sin(3+i) Homework Equations sin(x+y)= sinxcosy+sinycosx The Attempt at a Solution I think I am right in saying that you use the sine addition formula but then i get stuck from there. Is it something to do with exponential form?

Hello, Budding entrepreneur here looking for help. I've had this doubt for a long time. I can read the pump performance curves with respect to Head & Q. So if I have to select a pump that gives me 200 LPM @ 10 bar pressure, how do I select a pump from the curves. Is selecting a pump that...

Homework Statement Can anyone help me integrating (cosecx)^3 without using integration by parts? Homework Equations The Attempt at a Solution i couldn't get a clue how to do it,i used fundamental identity but always ended up like [∫(cosecx) dx] + [(∫(cotx)^2 . (cosecx) dx]...

hello friends,can you explain what is correct clearance of engine's moving parts,giving examples.

Here is the question: I have posted a link there to this thread so the OP can see my work.

Here are the questions: I have posted a link there to this thread so the OP can see my work.

Here is the question: I have posted a link there to this thread so the OP can see my work.

Hey all, Just a thought experiement here. With time dilation caused by gravity and relative velocity being a confirmed phenomena, do you think it's possible that other worlds that are extremely far away from each other, and are moving at a very high speeds relative to one another with...

what is the name of this part? what is the name of this component? thank you.

Homework Statement ∫x*cos(x^2) dx I tried using integration by parts, but the integral of cos(x^2) is very long, and I couldn't get it completely with my knowledge at the moment, so is there an easier way to solve this problem?

Hi guys, Stuck on an integration by parts question...Not going to post the question as I want to work it out myself, but as I'm a bit of a novice on diff/integration I'm stuck on what we do at a certain step of the process...anyway.. I know integration by parts we end up using ∫udv = uv -...

Integration by parts By repeatedly integrating by parts show that for $ n >1 $, $$ \int \frac{\ln^{n}(1-x)}{x} \ dx = \ln x \ln^{n}(1-x) + \sum_{k=1}^{n} (-1)^{k-1} \frac{n!}{(n-k)!} \text{Li}_{k+1}(1-x) \ln^{n-k} (1-x) + C$$ where $\text{Li}_{n}(x)$ is the polylogarithm function of order $n$.

Homework Statement Find the general solution of the equation (\zeta - \eta)^2 \frac{\partial^2 u(\zeta,\eta)}{\partial\zeta \, \partial\eta}=0, where ##\zeta## and ##\eta## are independent variables. Homework Equations The Attempt at a Solution I set ##X = \partial u/\partial\eta## so that...

What goes through an Engineer's mind upon designing a loudspeaker? Surely there must be some general guidelines, no? Perhaps. Although this is most likely dependent upon the circumstances (cost, enclosure, available power, etc). If these guidelines do exist, what are they. If you could order...

Homework Statement Show in detail that: \sigma_{x}^{2} = \int_{-\infty}^{\infty} (x -\bar{x})^{2} \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-X)^{2}}{2\sigma^{2}}} = \sigma^{2} where, G_{X,\sigma}(x) = \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-X)^{2}}{2\sigma^{2}}} Homework Equations \int u...

Here is the question: I have posted a link there to this topic so the OP can see my work.

I'm trying to integrate \int e^{4\ln{x}}x^2 dx I can't see using u-substition, x^2 isn't the derivative of e^{4\ln{x}} nor vice-versa. I tried integrating by parts and that didn't work. I used u=e^{4\ln{x}} and dv=x^2 dx I know I can't rewrite e^{4\ln{x}} as e^4e^\ln{x}

I'm following this example where it is asked to integrate \int \ln{x} dx using integration by parts. I don't understand how it's legal to set v=x since the only x in the equation is the argument of ln and that's already accounted for by u.