Integration Definition and 1000 Threads

Homework Statement ∫(t/√(1-t4))dt Homework Equations ∫(du/√(a2 - u2)) = arcsin (u/a) + C ∫(du/(a2 + u2) = (1/a) arctan (u/a) ∫(du/(u√(u2 - a2))) = (1/a) arcsec (|u|/a) The Attempt at a Solution Edit: I meant to write u where t2 is[/B]

Homework Statement Integrate Cosx/1+sinx dx from 0 to pi/2. "The question does not assume knowledge of integration by parts." Homework EquationsThe Attempt at a Solution Could it be found using the quotient rule? If not, is there any way of proving it without using integration by parts? Mod...

I greatly appreciate this chance to submit a query. I have the following integral: $$\int_{1}^t 2sin(t-\tau)e^{-2(t-1)} d\tau$$ and it has been suggested to me that if I sketch the two constituent functions and multiply them, I can read the answer off the paper. So here are my sketches: go...

Homework Statement [/B] ∫1/((x^1/3)-2)dx between b=666 and a=8 Aim is to prove divergence or convergence Homework EquationsThe Attempt at a Solution Okay so I know I can prove for 4x1/3 < x when 8 < x but I don't know where to go from here. There is obviously very large terminal values, and...

I always wondered that what is the physical interpretation of integration . How come integrating position gives as velocity? Can some one explain me what is physical insight of integration ? Ignore my poor communication skills.

When one uses a contour integral to evaluate an integral on the real line, for example \int_{-\infty}^{\infty}\frac{dz}{(1+x)^{3}} is it correct to say that one analytically continues the integrand onto the complex plane and integrate it over a closed contour ##C## (over a semi-circle of radius...

Homework Statement Integrate (4x+1)^1/2 Homework Equations Integration (ax+b)^n dx= (ax+b)^(n+1)/ a(n+1) The Attempt at a Solution (4x+1)^(3/2)/ 4(3/2) = (4x+1)^(3/2)/6 but the actual answer is 3(4x+1)^(3/2)/8

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] 1) ∫ dx/((x^(2))(x^(2)+4)^(1/2))2) I'm really stumped on this integral. I've tried several different methods of integration, but I kept getting stuck.3) The problem doesn't look like it...

I am interested to find the length shown in red in the attached figure. I want this length as a function of d (shown in blue) and the angle θ. Then I will integrate this length to dθ from 0 to π/2. Firstly, I used the law of the triangle to determine the length s which when subtracted from the...

Homework Statement HI people, I was trying to derive the stefan-boltzman law from the planc's formula, I kind of got stuck with an integral Homework Equations $$ \int_{0}^{\infty} \frac{x^3}{e^x -1} dx $$ The Attempt at a Solution I tried simplifying it with $$ \int_{0}^{\infty} x^3...

Hi I'm working on a GPS/INS model. Now I developped the mecanization equations for the INS. I have a kalman filter which estimate the error state (position error with respect to north and east). it takes as an input the diffrence between GPS and INS and gives its estimation . I have...

Homework Statement I am told to find out the length of he curve y=¼x^2 Homework Equations The length of the curve should be ∫√(1+¼x^2)dxThe Attempt at a Solution I substituted tanx and got ∫2/cos^3x dx So how could I continue and work out the solution? Should I use integration by part, or I...

Find the second degree polynomial P(x) that has the following properties: (a) P(0)=1, (b) P'(0)=0, (c) the indefinite integral ∫P(x)dx/(x^3(x-1)^2). Note: the the indefinite integral is a rational function. Cannot have Log terms occurring in solution. first. I use the generic polynomial...

Homework Statement Hi I have a really hard time understanding when and how to use the Power rule when integratingMy book states that if u is a function of x, then the power rule is given by: ∫urdu = (ur+1)/(r+1)+c First: I do understand that if u=2x Then the differential du=u'(x)dx =2 So...

Hi, I'm trying to solve ∫(x2-1)/(1+x2)*1/(1+x4)(1/2)dx I'm apparently meant to get some non-complex result, the question suggests to use the substitution u2 = x2 + 1/x2 But I haven't gotten anywhere with this. Any methods or suggestions (or the solution) would be much appreciated! Thanks

Homework Statement The parabola y = 6x - x^2 meets the x-axis at O and A. The tangent at O and A meet at T. Show that the curve divides the area of the triangle OAT into two parts in the ratio 2:1. Homework EquationsThe Attempt at a Solution Here is my working with my sketch. So I thought I...

Homework Statement While integrating by parts( by the formula) why don't we consider the contant of integration for every integral in the equation. Homework Equations $$∫uv = u∫v - ∫ ∫v . d/dx(u) $$ The Attempt at a Solution [/B] example. $$∫x \sin(x) dx = ?? $$ this is can be done like...

Say we have a function of the form f(x)=\bigg\lbrace\begin{matrix}c \qquad\quad\text{x=0}\\ 0\quad\text{elsewhere}\end{matrix} If we then integrate this over all space i.e. \int_{-\infty}^{\infty}f(x)dx Why does the result equal zero?

This is a seemingly simple question, though I'm not exactly sure where I'm going wrong (if in fact I am going wrong). To start off: you have a 2D un-normalized Gaussian function centred at the origin and with a sigma of 4. If you integrate it over a circle of radius 4 also centred at the...

Kindly can someone tell me how can i integrate and plot the following formula as a function of time. while theta is changing from 1 to 20. also attached .docx file for convenience. Any kind of help or advice will be highly appreciable.

Hello, I found something surprising (at least to me) while looking at the following integral: \int \sqrt{\frac{e^x-1}{e^x+1}} dx Wolfram Alpha suggests the following substitution as the first step: u = \frac{1}{e^x+1} Which leads to the following integral: \int \frac{\sqrt{1-2u}}{(u-1)u} du The...

Hi, I am working on Solar systems in Australia. I want to know the Australian standards for grid connected PV systems for voltage, power factor, reactive power etc.

I want to make sure I understand how to deal with discontinuities when they lie within an interval of integration. Infinite Discontinuities In this case, do we always resort to improper integrals? Jump Discontinuities If there is a finite number of jump discontinuities in the integration...

Hello dear physics masters on earth, I am very grateful to be priviliged to ask you a question regarding electric fields and potential of a single-cpin helix. It is portrayed as below. It is a line of uniform charge, and 1-turn helix with radius R and height H. I have came to ugly answers, and...

so ## \int wdw = \frac{1}{2}w^{2} ## now if w=x+y, ## \int (x+y)(dx+dw)= \int xdx + \int ydx + \int xdy + \int ydy ## which can be evaluated and gives ##\int(x+y)(dx+dy)=\frac{1}{2}x^{2}+2xy+\frac{1}{2}y^{2}## but ##\frac{1}{2}x^{2}+2xy+\frac{1}{2}y^{2} \neq \frac{1}{2}w^{2}## can...

I have no experience working with mice models, but why, for example, in pronuclear injection (or even other methods of transgenesis), is the injected gene of interest randomly integrated? In other words, why would the integration site of the DNA not be known or in a targeted region? I apologize...

In the Stoner-Wohlfarth model, a uniaxial, non-interacting particle is cooled to very low temperature with no exposure to an external field. Therefore, the orientation of each particle is random, if you have a group of particles. In their paper, they integrate such that: \langle \cos (\Theta...

Look, I was wondering if substituting the variable more than once is valid and hence the definite integral intervals change this way. Consider the following integral (I'm working for finding the volume of a solid of revolution): *\pi \int_{-3}^{5}3^{2}-(\sqrt{\frac{y+3}{2}}+1)^2dy Personally I...

What is the difference between \int_{-\infty}^{\infty} \frac{x}{1+x^2}dx and \lim_{R\rightarrow \infty}\int_{-R}^{R} \frac{x}{1+x^2}dx ? And why does the first expression diverge, whilst the second converges and is equal to zero?

I have the following integral \int e(2x) cos(ex). Let u = ex Do integration by parts: \int u2cos(u) du = u2sin(u) - \int (2usin(u) du Do integration by parts again for \int (2usin(u) du: \int (2usin(u) du = -2ucos(u) - \int -2cos(u) du Putting it all together: \int e(2x) cos(ex) =...

Hi everyone, today I came across a problem at work that requires integrating this function (indefinitely, with respect to c): \frac {1} {\sqrt {(k+p-c)^2 + 4 k c}-k-p+c} k, p and c are all real and positive. I submitted it to Maxima, but it stayed implicit. Can you please suggest any...

Hi, I have a problem of integration in Matlab. I want to integrate the following equation: y=x/(exp(x)-1) and x is from 0 to 1. I use int(y,0,1), but it seems that it does not give correct result. Could you help me how to do it in Matlab? Thanks!

I have come across the following integral in my PhD research. \int_{-L_y/2}^{L_y/2}\int_{-L_x/2}^{L_x/2}e^{2 i k \sqrt{(d \cos\theta + x)^2+(d \sin\theta + y)^2}}dxdy Ultimately, x and y are integrated out and I will be left with a function of ##\theta##. I am doing this the following way...

Homework Statement I'm going to cut from the initial part of the problem, which I am confident is good to go, and cut straight to the antiderivatives. Homework Equations All antiderivatives are to be integrated on the interval from 0 to π/18 (I1) = -1/9 cos 9x - (I2) (-2/27 * cos3(9x)) + (I3)...

It is posted here http://math.stackexchange.com/questions/1290380/how-to-integrate-hydrostatic-force-on-a-two-dimensional-shape and I would really appreciate some insight on this question. I sliced the sections horizontally and could not get the answer.. thank you!

I have this exercise, where I am to integrate out the fluctuations in the order parameter δρ, but I don't really know how to do this. The integral is over r and imaginary time. Should I try to complete the square, so the correlation term between δρ and Θ drops out? In that case which shift of...

Homework Statement I am trying to work out the Fourier coefficient a_{n} for : Mathematics is not my strong point and I would appreciate some help. The answer that wolfram spits out it lovely and neat and I am struggling to get my answer to it. Homework Equations The Attempt at a...

I'm curious if there is a heuristic or method to determine the inner and outer radii as used in the Washer Method, WITHOUT needing to graph anything?

Homework Statement find the acceleration due to gravity at the centre of a solid hemisphere. Homework Equations ##F=\frac{GMm}{r^2}## The Attempt at a Solution i decided to go for cylindrical coordinayes (which is way beyond my syllabus). I did some research though. let me take a point...

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...

$$\int x^2\cos(mx)\,dx$$ When integrating this by parts, the $x^2$ will become the $u$ and the $\cos(mx)\,dx$ will become $dv$. How is the $\cos(mx)$ integrated if there are two variables?

Homework Statement Movies are always chock-full of scientific inaccuracies. As educated people, it’s our duty to ruin all the fun of it by taking the time to work out what should happen. For this problem, let’s look at the transport in the 2012 remake of “Total Recall.” In the movie, there are...

Anyone know how to integrate this? ##\int{\frac{(1 + x^2)}{(1 - x^2)\sqrt{1 + x^4}}dx}## Please give me a hint as I even don't know what to do.

Homework Statement The problem is actually from chemical kinetics, but my problem is solving the differential equation obtained. (dx(t))/(dt) = -j*x^2-k*x+k*a ; x is a function of t, and j,k,a are all real positive constants. Homework Equations I know this is a Ricatti type equation. But this...

Homework Statement [/B] Keep in mind this is a Top Gun-themed homework assignment. Cougar comes in for a shaky landing. His 20422 kg airplane traveling at 85 m/s strikes the deck at 3.5 degrees below the horizontal. Cougar's plane snags the landing cable stretched across the deck. The landing...

Hi! Here is my task: Find inverse z transform of $$X(z)=\frac{1}{2-3z}$$, if $$|z|>\frac{2}{3}$$ using definition formula. I found that $$x(n)$$ is $$\frac{1}{3}(\frac{2}{3})^{n-1}u(n-1)$$ (using other method). But how can I find it using definition formula, $$x(n)=\frac{1}{2\pi j}\oint_{C}^{ }...

Homework Statement Given two curves y=f(x) passing through (0,1) and ##g(x)=\int\limits_{-\infty}^xf(t)dt## passing through (0,1/n). The tangents drawn to both curves at the points with equal abscissae intersect on the x-axis. Find y=f(x). Homework Equations None The Attempt at a Solution...

Liquid is flowing into a small tank which has a leak. Initially the tank is empty and, t minutes later, the volume of liquid in the tank is V cm3 . The liquid is flowing into the tank at a constant rate of 80 cm3 per minute. Because of the leak, liquid is being lost from the tank at a rate...

Homework Statement Consider the following geodesic of a massless particle where ##\alpha## is a constant: \dot r = \frac{\alpha}{a(t)^2} c^2 \dot t^2 = \frac{\alpha^2}{a^2(t)} Homework EquationsThe Attempt at a Solution Part (a) c \frac{dt}{d\lambda} = \frac{\alpha}{a} a dt =...

Does integrating find the area between the curve and x-axis (regarless of it being a smile/frown or any other graph)? I've heard people say its the area UNDER a curve... but then how would you even get a definit answer surely it may be infinite if there's no restrictions? Thanks