Integration Definition and 1000 Threads

Homework Statement I am trying to work the moment of inertia for a) rotating rod, axis through the centre of the rod http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod3 b) Solid cylinder http://hyperphysics.phy-astr.gsu.edu/hbase/icyl.html#icyl2 [/B] Homework Equations I = R^2 dM The...

Please help me with this question. Part a was good but I don't understand parts b or c. Thanks in advanced.

This is the integral: http://www.wolframalpha.com/input/?i=integrate+x%5E2%2Bxy%2F2+from+0+to+x+with+respect+to+y But my calculator (TI-nspire cx CAS) gets this: x*(2x^2+xy)/2 Any idea why this is?

Homework Statement An airplane flies from the North Pole to the South Pole, following a winding trajectory. Place the center of the Earth at the origin of your coordinate system, and align the south-to-north axis of the Earth with your z axis. The pilot’s trajectory can then be described as...

Homework Statement The question says: f (x)=x2+7x +∫0x(e-tf (x-t)dt. Find f (x). Homework Equations None The Attempt at a Solution What I did is: Consider the integral: I=∫0x (e-tf (x-t)dt We know that ∫abf (x)dx=∫abf (a+b-x)dc So using it here: 1/ex∫0xetf (t)dt----(1) Leaving the "1/ex...

Homework Statement Evaluate the triple integral: ∫ x dxdydz A where A = {(x; y; z) : x, y, z > 0, x + y + z ≤ 1} . Homework Equations None that I know of. The Attempt at a Solution The problem I have is determining the limits for x, y and z. I don't really understand the following...

$\int x\ \cot^2\left({x}\right) dx $ $u=x$ $dv=\cot^2\left({x}\right) dx $ $du=\frac{x^2}{2}$ $v=\frac{-\cos\left({x}\right)+x\sin\left({x}\right)}{\sin\left({x}\right)}$

what is the relationship between special functions and integration ? why integral of some function like (sqrt(ln(x)) and (cos(1/x) and more) are entering us to special functions?? PLEASE HELP ME TO UNDERSTAND.

Does this integration of Ricci scalar over surface apply in general or just for compact surfaces? ∫RdS = χ(g) where χ(g) is Euler characteristic. And could anybody give me some good references to prove the formula?

Homework Statement $$\int\frac{x^2+3}{x^6(x^2+1)}dx$$ Homework Equations None The Attempt at a Solution I easily got the answer using partial fractions by splitting the integral as ##\frac{Ax+B}{x^2+1}+\frac{C}{x}+\frac{D}{x^2}+\frac{E}{x^3}+...+\frac{H}{x^6}## and then finding the...

Homework Statement Perform a Monte Carlo integration of: ∫ xdx/(2+3x)^2 with the bounds of 0 and 1 on the integral You should use 10 trials of at least 100 data pairs per trial and average the result I guess I am supposed to generate a x and y random number between 0 and 100 and if the...

Ok so what I want to know is, is this valid? If so what does it mean?

Homework Statement [/B] A shark will in the direction of the most rapidly increasing concentration of blood in water. Suppose a shark is at a point x_0,y_0 when it first detects blood in the water. Find an equation for the path that the shark will follow by setting up and solving a...

Homework Statement I am given the wave eqtn: (\frac {d^2} {dr^2}+\frac{1} {r} \frac {d} {dr})\Phi(r)=−k^2\Phi(r) The problems asks to 'show that the substitution $$ \Phi=r^{-\frac{1} {2}} \phi $$ gives an eqtn for which the Numerov algorithm is suitable'. Homework EquationsThe Attempt at a...

I have an Integral that is convergent over the range (-inf, Lambda) where 0< Lambda < 1. I need to change variables to move this to (0.1, 0.9) in such a way that I do not introduce any poor behavior, such as asymptotes or discontinuities as it needs to be well behaved. Is there a standard...

1. I need to find a condition that the equation will have a integration factor from the shape K(x*y). (K-integration factor sign) 2.the eq from the shape M(x,y)dx+N(x,y)dy=0 ,not have to be exact!3. i tried to open from the basics. d(k(x*y)M(x,y))/dy=d((k(x*y)N(x,y))/dx. and i used the fact...

Hi guys! I am reading the book "Gravity" by Hartle. I came across this scary-looking integral. The author does integration by parts and I don't get how he does it. Could someone guide me please? Relevant equations: ∫u dv = uv - ∫v du

Homework Statement integrate from 1 to 2 x(x^2-3)^(1/2) with respect to x. Homework EquationsThe Attempt at a Solution i attempted using numerical approximations but at x=1, the function is not defined so is there a way to combine improper integrals with this? Aceix.

Homework Statement Evaluate the integral of (x+1)5^(x+1)^2 Homework EquationsThe Attempt at a Solution I set my u=(x+1) making du=1dx. This makes it u*5^u^2. I integrated the first u to be ((x+1)^2/2) however I don't know what to do with the 5^u^2

Homework Statement integrate Homework Equations please solve this using methods only like 1. Substitution 2.Partial fraction 3.By Parts The Attempt at a Solution i have tried all the above three methods mainly using substitution and by parts... i have expanded the a^3 - x^3 and then kept...

Homework Statement integrate 1/(1+e^x) dx Homework EquationsThe Attempt at a Solution firstly i let t=1+e^x and then i come to : integrate 1/(t^2-1) and then i put t=secx . . . but then the final ans is -1/2 ln | 2/e^x +1 | it should be 1 instead of 2, i hv checked for the steps for so many...

Homework Statement ∫ [x^(3)+4] / [x^(2)+4] dx Homework Equations N/A The Attempt at a Solution I know that the fraction is improper, so I used long division to rewrite it as x+(-4x+4)/[x^(2)+4]. Given the form S(x)+R(x)/Q(x), Q(x) is a distinct irreducible quadratic factor [x^(2)+4]. I used...

Homework Statement Calculate the magnetic field of a current loop. Compare your numerical results with exact solution above the center of the loop. Investigate the effect of the grid size based on this comparison. Homework Equations dB = u0*I/4pi * (dL * R) / (R^2 + Z^2)^3/2 Bz = u0*I*R^2/ (2...

Hi There, I'm a new member, so apologies if I've posted this in the wrong area. I've been working through the ASME STS-1-2006 Steel Stack Standard, particularly the Vortex Shedding section. I've come across this nasty integral which is doing my head in, and we wondering if anyone would mind...

In all the notes that I've found on differential geometry, when they introduce integration on manifolds it is always done with top forms with little or no explanation as to why (or any intuition). From what I've manage to gleam from it, one has to use top forms to unambiguously define...

Homework Statement $$\int_0^{\pi/2}(sinx-cosx)ln(sinx)dx$$ Homework Equations ##int_0^af(x)dx=int_0^af(a-x)dx## The Attempt at a Solution Using above equation, you get (without integral sign): ##(sinx-cosx)ln(tanx)## but it did not make any difference. I got the answer by splitting the...

Hello, sorry for this stupid question. I struggled to find the moment of inertia of half solid thin disk (about the center of the disk) through an integration, but I couldn't get the right value. I'm pretty sure it has to be MR^2/4, but I=\int r^2 dm \\ dm=(M/A)dS With A=\pi R^2/2 I compute...

So I stumbled upon ∫1/(x^4) , and by applying the power rule , the answer is: -1/(3x^3) Why's that? Sorry for bothering you guys with such a beginner question!

Homework Statement Integral of ∫1/x^2 (or ∫x^-2) between 1 and 0.The Attempt at a Solution I can integrate it no problem to give me -1/x or x^-1, but when I put it between the limits of 1 and 0 I get ∞-1 which is just ∞. Is this right or do I need to use L'Hopital's rule. If so, how? I'm...

Homework Statement In this lab various thicknesses of a few materials are placed between a source of gamma radiation and a couple different detectors. It is reasonable to assume that some small change in the thickness of the shielding would produce a proportional change in the intensity of the...

I have been trying to solve an integration that i have I am not even sure if it's possible. Here, A, m, alpha, a these are constants. I have tried few methods, but couldn't find any way out. I would appreciate any help.

Homework Statement Homework EquationsThe Attempt at a Solution i got ln(x-2) but not sure what to do with the 4[/B]

First of all, apologies as I've asked this question before a while ago, but I never felt the issue got resolved on that thread. Is it valid to prove that \int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx using the fundamental theorem of calculus (FTC)?! That is, would it be valid to do...

For example, $$\int \frac{e^x}{3e^x-1}dx$$, Should I write my answer in this $$\frac{1}{3}\ln (3e^x-1)+c$$ or $$\frac{1}{3}\ln \left | 3e^x-1 \right |+c$$ ?

Homework Statement Integral of $$ x^3\sqrt{x^2+16}dx $$ answer should give $$ 1/5(x^2+16)^{5/2} -16/3(x^2+16)^{1/2}+C $$ Homework Equations x=atanθ The Attempt at a Solution Mod note: The integral is ##\int x^3 \sqrt{x^2 + 16} dx## The published answer is ##1/5(x^2+16)^{5/2}...

Suppose $f$ is a continuous function on $(-\infty,\infty)$. Calculating the following in terms of $f$. $$\lim_{{x}\to{0}}f\left(\int_{0}^{\int_{0}^{x}f(y) \,dy} f(t)\,dt\right)$$

Homework Statement So, I have a trigonometric substitution integration problem. The working is rather hairy, but I've gotten to the point where you draw the triangle to express theta in terms of x. But that's where I'm stuck! I think I may be having trouble with the constant of integration...

In this problem, I need to find the trajectory of a particle (as a function of time) which moves at a speed 's' but also turns at an increasing rate; angular acceleration α. The trajectory looks like a spiral which converges to a point. The particle has an initial position vector p and a...

Homework Statement 1.\int{\frac{sinx}{1+cos^{2}x}} \, dx 2.\int{\frac{1}{13-4x+x^2}} \, dx Homework Equations Inverse trig identities. The Attempt at a Solution For the first one, I'm not too sure about what to do with the sinx on the numerator and i have tried u-substitution to no avail...

Homework Statement (Just for number 1 only - finding electric field) [/B] Homework Equations dE = k dq/R^2 sin theta = y/R = y / sqrt (a^2 + y^2) dq= lamda*dy The Attempt at a Solution [/B] I'm confused at the point of calculating the integral from -L/2 to L/2. I got the final integral...

relation between integration and differentiation ? how is instantaneous slope(differentiation) related to area under the curve(integration) ? thank you!

Homework Statement Two arcs of charge are center at the origin. The arc at radius r has a linear charge density of +(lambda) while the arc of radius 2r has a linear charge density of -(lambda). (r = 5cm, lambda = 1nC/m, theta = 40°) a) Calculate the magnitude and direction (as an angle from...

In Jackson's 'classical electrodynamics' he re-expresses a volume integral of a vector in terms of a moment like divergence: \begin{align}\int \mathbf{J} d^3 x = - \int \mathbf{x} ( \boldsymbol{\nabla} \cdot \mathbf{J} ) d^3 x\end{align} He calls this change "integration by parts". If this...

Homework Statement What type of region(s) do the following classify as? Homework EquationsThe Attempt at a Solution I would classify D1 as both types; my reasoning is that by the definition of a convex polygon (i.e. all x,y in D1, the lie segment connecting x and y is entirely in D1), this...

Homework Statement ∫dt/(t^2 +2tcos a + 1) (Limits of the integral are from 0 to 1) (0<a<π) Homework EquationsThe Attempt at a Solution Put t=sin a dt=cosa da ∫dt/(t^2 +2tcos a + 1) = ∫cos a da/(sin^2 a + sin 2a + 1) [ limits of integration changed to 0 to π/2] = ((cosec a)/2) ∫sin 2a da/(sin^2...

Hello everyone, I have a question about integrating in Laplace Transform. For example, if I have: f(t)=e^{i.t} I have to solve this equation: \int_{0}^{\infty}e^{i.t}.e^{-s.t}dt If I do like this, it's very simple...

Homework Statement Suppose a constant force F acts on a particle of mass m initially at rest. (a) Integrate the formula for acceleration \vec{a} = \frac{\vec F}{\gamma m} - \frac{\vec v}{\gamma mc^2}(\vec F \cdot \vec v) where \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} to show that the speed...

Homework Statement the integral of x^3 (x^2 + 20)^1/2 Homework Equations use u substitution The Attempt at a Solution I think I have finally figured the problem out, can you confirm if this is the correct answer please? u=x^2 +20 x= sqrt(u-20) du= 2x dx integral of x^3 * sqrt( u) du/2x...

Recently I started seeing integral calculus and right now we are covering the topic of the antiderivative. At first sign it was not very difficult, until we started seeing integral variable substitution. The problem starts right here: Let's suppose that we have a function like this: \int...

Homework Statement The question involves finding the arc length of the parametric equation x = e^t + e^-t and y = 5 - 2t Homework Equations Arc length of a parametric equation ∫√(dy/dt)^2 + (dx/dt)^2 dt limits are from 0<t<3 The Attempt at a Solution Taking the derivative of both x and y...