Integration Definition and 1000 Threads

so i know I've asked this question before but id really like a step by step walk through with a few questions. starting with $\int_{\pi/3}^{\pi} \ \sqrt{1+\frac{4}{x^2}},dx$ i know I am not showing any work but id like to see how to this can properly be done. thanks wait never mind i think i...

I'm making this new post in the general math section since I don't know what field of math this question belongs to anymore. So the picture I currently have regarding the abstractions of integration and differentiation from single variable-calculus to multi-variable calculus is that the...

(Wave)I have a test tomorrow on the different Techniques of Integration: integration by parts, partial fractions, trigonometric integrals, trigonometric substitutions, improper integrals and i want to fully understand them. I've been working on problems from the book but can someone just give a...

Im supposed to use integration by parts for this problem but i understand how to. $$\int \ \frac{xe^{2x}}{(1+2x)^2},dx$$

please help! this homework assignment is due in like 3 hours and i have to get it done. $$\int \frac{1 \, dx}{(x^2+8x+17)^{2}}$$ $$\int_{-1/ \sqrt{3}}^{1/ \sqrt{3}} \frac{e^{arctan {y}} \, dy}{(1+y^2)}$$ i need to see all the steps. do i use partial fractions for the first one?

Hey, I was just wondering if there was a way to prove the power rule for integration using the definition of a definite integral. And I don't mean using the proof for the differentiation power rule, I mean is it possible to derive \displaystyle\large\int_a^b x^c=\frac{b^{c+1}-a^{c+1}} {c+1}...

Homework Statement Why can't you do integration-by-parts directly on the middle expression in equation 1.29--pull out the time derivative over onto x, note that \displaystyle \frac{\partial x}{\partial t} = 0, and conclude that \displaystyle \frac{d \langle x \rangle }{dt} = 0Homework Equations...

I have a few questions about the generalizations of concepts like integration and differentiation of single-valued functions of a single variable to vector-valued functions of several variables. All in the context of real analysis. Beginning with scalar-valued functions of several variables...

Homework Statement Find the electric field a distance z from the center of a spherical surface of radius R which carries a uniform density σ. Treat the case z<R (inside) as well as z>R (outside). Express the answers in terms of the total charge q on the sphere. Homework Equations E = \int...

How to integrate: _{2}F_{1}(B;C;D;Ex^{2})\,Ax where _{2}F_{1}(...) is the hypergeometric function, x is the independent variable and A, B, C, D, and E are constants.

Hi all, I need help with numerical solution of motion equation. From the numerical point of view and in the real of the finite element method, which method is recommended for the solution of damped ( proportional damping) linear motion equation? I have been trying three common methods; Modal...

Dear all, I am mechanical engineer with no background to circuitry and electronics. I am trying to connect a flow switch ( using hall effect ,12 dc input) and I want it to trigger a piezo alarm (12V dc) when water flow stops. There are three wires from the flow switch, two for power and...

Homework Statement ∫(x2)/(ex/2) dx Homework Equations The Attempt at a Solution I'm not completely sure where to start on this one. I don't see any sort of u substitution working, would integration by parts be a good idea? Maybe let u=x2 and dv=(1/ex/2) ?

I need to compute numericaly n-body sys. interacting acording to the Weber force: http://en.wikipedia.org/wiki/Weber_electrodynamics and I have a problem with the acceleration on rhs: r'', because the acceleration is unknown, due to the Newton law: F = ma, and we need just 'a' to do next...

If ##\omega## is an exact form ##( \omega = d\eta )## and ##\Omega## is the region of integration and ##\partial \Omega## represents the boundary of integration, so the following equation is correct: $$\\ \oint_{\partial \Omega} \omega = 0$$?

Homework Statement ∫x^2√(2+x) using u sub Homework Equations ∫x^2√(2+x) The Attempt at a Solution I can't seem to find anything to use for a u sub. if I sub 2+x I just get 1, and if I sub x^2 I just get 2x If I do √(2+x) I just get 1/2(1/√(2+x))

I encountered this when I tried to evaluate the following integral with help of complex numbers. $$\int_0^{\infty} \frac{dx}{x^2+1}$$ The answer is obviously $\pi/2$ as the integrand is derivative of $\arctan(x)$. Now, I tried it it using partial fraction decomposition: $$\int_0^{\infty}...

Hi I'm trying to integrate the following q_m = -D A \frac{dc}{dx} where A = 4 \pi r^2 Yes, a sphere.My supplied literature simplifies to q_m = -D 2 \pi r L \frac{dc}{dr} when A = 2 \pi r L Integrating to \int_{r1}^{r2} q_m \frac{dr}{r} = - \int_{c1}^{c2} 2 \pi L D dc Integrated to q_m ln...

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...

Homework Statement ∫1/(3+((2x)^.5))dx the answer should be ((2x)^.5) - 3ln(3+((2x)^.5)) + c I keep getting ((2x)^.5) - ln(3+((2x)^.5)) + c Homework Equations ∫1/(3+((2x)^.5))dx The Attempt at a Solution I did: u = 3 + ((2x)^.5) du = 1/((2x)^.5) dx du((2x)^.5) = dx...

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...

Hello. I am not confident about this question. I think I have to use cauchy integral formula. But before that, I should decompose the fraction, right? Or is there a simpler way to do it?　A friend told me that each contour only had one pole interior to it so he just used the Cauchy integral...

Hello. I am not confident about this question. I think I have to use cauchy integral formula. But before that, I should decompose the fraction, right? Or is there a simpler way to do it?　A friend told me that each contour only had one pole interior to it so he just used the Cauchy integral...

Hi, I need to calculate area of an irregular polygon which can be of any complex shape numerically i.e. using numerical integration techniques. Please can anyone suggest any reference material / best way of going about this efficiently? Akash

a) We know that the smallest charge that can exist is 'e' . But in several instances (such as calculating potential energy of sphere of charge ) we consider 'dq' and then integrate it . How can we justify this ? b) We know that 1/2 or 1/3 of e (charge of electron) doesn't exist . But...

Numerical integration methods applicable to a type of definite integrl Hey, so I've been working on a program to numerically integrate an integral of the form ∫xnf(x) dx, LIM(0 to INF.) Here n can go to negative non integral values, say -3.7 etc. and f(x) is a function of sin, cos and...

I am trying to compute the following integral: \int \exp^{w^T \Lambda w}\, d\theta where \Lambda is a constant wrt \theta w = y - t(x, \theta) So, I am trying to use substitution and I have: d\theta = \frac{-dw}{t^{'}(x, \theta)} So, substituting it, I have the following integral...

in this video , the prof had to integrate x/(a^2+x^2)^3/2 , i know we usually do this using substitution , but in the video...he ignored the x and integrate like it was 1/(a^2+x^2)^3/2, how does that work?

Homework Statement it is capacitor charging expression..how to find its integration Homework Equations VL(t) = ∫_(T/2)^T▒〖Vme^(-T/2RC) 〗 dt The Attempt at a Solution result is 0.5...but how

So I'm doing length of an arc in my calculus 1 class. After plugging everything in the arc length formula. Now I have this complicated function to integrate. Square root of (16x^8+8x^4+1)/16x^4. I took the denominator out of my square root and got 4x^2. Now I take u=4x^2. Du/2x =dx...

Homework Statement Find the indefinite integral of the below, using partial fractions. \frac{4x^2+6x-1}{(x+3)(2x^2-1)} Homework Equations ?The Attempt at a Solution First I want to say there is probably a much easier and quicker way to get around certain things I have done but I have just...

Homework Statement for -1≤x≤1, F(x) =∫sqrt(1-t^2) from -1 to x ( sorry don't know how to put the limits on the sign a. What does F(1) represent geometrically? b. Evaluate F(1) c. Find F'(x) Homework Equations The Attempt at a Solution Since my teacher never seems to give...

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?

Can you check my work please, Compute $\displaystyle \int_{|z|=1} |z-1| . |dz| $ $ z(t) = e^{it} , 0 \leq t < 2 \pi $ $ |dz| =| ie^{it} dt | = dt $ $\displaystyle \int_{0}^{2\pi} |\cos(t) + i\sin(t) - 1 | dt $ $\displaystyle \int_{0}^{2 \pi} \sqrt{(\cos(t) -1)^2 + \sin ^2( t)} \, dt =...

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 Integrate dx/((x^2+1)^2) Homework Equations Tan^2=sec^2-1 The Attempt at a Solution So I let x=tanx then dx=sec^2x Then plugging everything in; Sec^2(x)/(tan^2+1)^2 So it's sec^2/(sec^2x)^2) which is sec^2x/sec^4x Canceling out the sec^2 gives...

Homework Statement I want to take an antiderivative of a function with respect to x. But in addition the function includes a term y (x) that is a function of x itself. Do I have to apply the reverse power rule also to y(x) also? The integral can be seen as an indefinite. Homework...

1. The problem statement, all variables and given/known Show that ∫∫∫ 12y^2 z^3 sin[x^4] dxdydz Region: { y< x< z 0< y< z 0 <z< (Pi)^ 1/4 Equals Pi/4 Change order of integration to dydxdz 2. Homework Equations Order of integration 3. The Attempt at a...

Homework Statement for this question, my ans is pi/2 not pi/4 . can anybody please check where's the mistake? Homework Equations The Attempt at a Solution

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?

Homework Statement for this question, the question only stated SUITABLE substituition, what substituition should i use? this substituion does not involve trigo functions , am i right? P/S : I'm just asking opinion, not the full working. Homework Equations The Attempt at a Solution

Homework Statement Homework Equations ∫∫∫dV The Attempt at a Solution Ok so I started by setting my bounds equal to √(200-x^2-y^2) ≥ z ≥ √(x^2+y^2), √(100-x^2) ≥ y ≥ -√(100-x^2), 10 ≥ x ≥ -10 which I got from solving z^2 = (200-x^2-y^2) = x^2+y^2 => x^2+y^2 = 100 but it...

Homework Statement for this Q and t are variables, 10 and surd k are constant, is my working correct? Homework Equations The Attempt at a Solution

Homework Statement Express the iterated integral ∫[0,1]∫[0,1-y^2]∫[0,y] f(x,y,z)dzdxdy a. as a triple integral (i.e., describe the region of integration); b. as an iterated integral in the order z, y, x; c. as an iterated integral in the order y, z, x: The Attempt at a Solution so...

1. The problem statement Fill in the blanks ∫ [0,1] ∫ [2x^2,x+1] f(y) dy dx = ∫ [0,1] ( ) dy + ∫ [1,2] ( ) dy The expressions you obtain for the ( ) should not contain integral signs. The brackets are the bounds of integration, and the open parenthesis are the blanks. The Attempt at a...

Homework Statement \int \frac{-2x + 4}{(x-1)^{(2)}(x^{(2)}+1)}Homework Equations The Attempt at a Solution I've done the problem a couple times but the answers keep coming out differently so I'm assuming I am messing up the setup. This is what I have for the first part of the setup: -2x +...

1. Find the volume of the region above the triangle in the xy-plane with vertices (0,0) (1,0) (0,1) and below the surface z =f(x,y)=6xy(1-x-y) My attempt is attached

Evaluate ∫∫(x^2 + y^2)dx dy over the region enclosed within R (0,0), (2,0) and (1,1). I am not asking someone to do the problem but to just verify, have I got the limits right? I split it up into 2 legs for the first leg integrate from , x: 0→1 and y :0→x for the...

Homework Statement Hi Guys, I need help to solve this double integration. This integration is over r and theta. The rest are constant. Homework Equations ∫^{R_{2}}_{r=0} ∫^{\pi}_{\theta=0} r^{2} sin(\theta) dr d\theta / ((D^{2}+r^{2} - 2rd cos(\theta))^{2} - R_{1}^2)^{3}, r from 0 to R_{2}...

I know this has been asked many times. I am integrating acceleration data from MEMS accelerometer to get velocity. I found an app note by freescale - http://cache.freescale.com/files/sensors/doc/app_note/AN3397.pdf It ignores the sampling time to calculate the area. The formula should...