Integrating Definition and 940 Threads

Homework Statement trying to integrate this: \int^{\theta}_{\theta_{0}} \sqrt{\frac{1-cos(\theta)}{cos(\theta_{0}) - cos(\theta)}d\thetaHomework Equations My book tells me to let theta = pi - 2gamma and then simplify from there but I'm just not seeing that ! any hints? is there a trig...

Homework Statement The actual question is asking for the normalization constant for the wavefunction \psi\left(x\right)=A\sin^{5}\left(\dfrac{\pi x}{a}\right) without carrying out integration In short they want me to find the value of A such that A^{2}\int_{0}^{a}\sin^{10}\left(\dfrac{\pi...

Homework Statement Multiply the given equation by the given integrating factor and solve the exact equation. Homework Equations ydx+(2x-yey)dy=0, \mu(x,y)=y. The Attempt at a Solution M=y2, N=2xy-y2ey Integrating N=\Psiy WRT x I get xy2-((1/3)y3ey + y2ey)+h(x)=\Psi(x,y) Differentiating...

I am working on the following problem but I am apparently not applying the integrating factor correctly: The DE is: dy/dt = e^(-t/20) - (1/40)y I moved the last term to the left, giving dy/dt + (1/40)y = e^(-t/20). I had e^(t/40) as my integrating factor. Going in my (wrong) direction, I was...

The title contains the problem I have difficulty with. I understand I must use u substitution and then integrate by parts. So my actual problem is: How do I find the derivative of arcsin(x^2) if u = arcsin(x^2)? I know the derivative of arcsin(x^2) is 1/(1-x^2)^1/2 Thanks for...

Homework Statement [1/(x^4 - x)]dx Homework Equations The Attempt at a Solution I factored the denominator to x(x-1)(x^2 + x +1) and I'm not sure if I can use partial fractions.

Homework Statement use an integrating factor to solve \frac{ \partial u}{ \partial x} = -2 + \frac{u}{2x} The Attempt at a Solution let P(x) = \frac {1}{2x} M(x) = e^(\int(\frac {1}{2x}dx)) = \sqrt{x} so u = \frac{1}{ \sqrt{x}}...

Homework Statement I have work these two problems, but in the first one #4 I feel like I'm missing something a step or something. and in the second problem I'm just lost, I can't finish it so will you please assist me. your help is appreciated. Homework Equations thanks a lot. The...

Homework Statement Integral of dx/[(x2 - 2x + 2)2]Homework Equations Trig substitution rules: for expression sqrt(a2 - x2) make x = asin(t) with -(pi/2) < t < (pi/2) for sqrt(x2 - a2) make x = asec(t) with 0< t < (pi/2) and for sqrt(a2 + x2) make x = atan(t) with -(pi/2) < t < (pi/2)The...

Hello All, Given the equation (2/y + y/x)dx + (3y/x + 2)dy I am first asked to show the equation is not exact. To do this I showed the mixed partials were not equal i.e.: (2/y + y/x)dy != (3y/x + 2)dx I am then asked to find an integrating factor and show the potential function is given...

how do i integrate 0.5e[SUP]t[SUP]

Hi, besides integration by parts, does anyone know of a simple integration trick to solve the integral (wrt x) of exp(x)*f'(x)?

Homework Statement Hey, I've been working through a book and one problem just gets me that I know should be a piece of cake. I don't know if I'm just being an idiot or not seeing something but the problem is to take int e^(ax)cos(bx)dx and int e^(ax)sin(bx)dx simultaneously by multiplying the...

0 \leq r \leq 1 -1 \leq z \leq 1 0 \leq \theta \leq 2\pi \int\int\int dV where dV = r dr d/theta r = 1 - z2 weird huh?

Homework Statement the problem is attached Homework Equations The Attempt at a Solution I don't understand to the Q but what i did is just integrating the dose rate , the Q is not clear to me can anyone help me

I'm really confused with how to prove this result...could anybody help please? Let I_{1} be the line segment that runs from iR (R>0) towards a small semi-circular indentation (to the right) at zero of radius epsilon (where epsilon >0) and I_{2} a line segment that runs from the indentation...

I'm not understanding why my answer is wrong Homework Statement \inttan^3(x) dx This is the solution I've been getting for this problem, but I notice you get a different answer when you let u = tan(x) and du = sec^2(x) dx Homework Equations tan^2(x) = (sec^2(x) - 1) The Attempt at a Solution...

Homework Statement INTEGRATE dx / (2 * root(x)) * (1 + x) Homework Equations That's pretty much it! The Attempt at a Solution I received this question on a Calc II exam, so I'm only looking for the solution for my own understanding (I'm sure I already got it wrong). My instinct...

Homework Statement xy' - 4y = x4ex Homework Equations The Attempt at a Solution y' - 4x-1y = x3ex x-4y' - 4x-5y = x-1ex I'm not sure what to do next, I can't express the LS as a derivative

Homework Statement Let P(v) represent the Maxwell-Boltzmann speed distribution. Basically what it comes down to is that I have to find the definite integral (0,inf) of P(v)*v^2 and get vrms from this. Homework Equations We are given the definite integral from 0 to inf for the function...

greetings what does a integrating factor tells about a differential equation? in order to find the solution for a exact equation we multiply the equation by integrating factor(I.F). as intergrating factor=e^integration(p)dx i.e given by I.F=e^gx where gx is integration of p now as we have...

Homework Statement [PLAIN]http://img580.imageshack.us/img580/9506/linegu.jpg The Attempt at a Solution Parametrising the curve C_1 as follows: {\bf p}(t) = (1-t)(1,4) + t(3,3) = (1+2t,4-t) {\bf p}'(t) = (2,-1) So \int_{C_1} = \bigg\{ \sqrt{\frac{y}{x}} \frac{dx}{dt} +...

By setting u = sin(x), I got 1/2 (sin(x))^2 By setting u = cos(x), I got -1/2 (cos(x))^2 The two answers are not the same, why are there two solutions?

Homework Statement Given that the probability of finding a 1s electron in a region between r and r + dr is: P = \frac{4}{a_{0}^{3}}r^{2}e-2r/a0dr work out the probability that an electron would be found within a sphere of radius: i) a0 Homework Equations The Attempt at a...

Homework Statement Hi Say I have the function f(x,y) = xy, and I want to integrate f(x,y) from (0,0) to some (px, py), where I know p^2 = p_x^2+p_y^2. What I have done is to write p_x ^2 + p_y ^2 = p^2 so the limits for px run from \pm \sqrt {p^2 - p_y ^2 }. Now, how about the limits...

For integrating over type 1 and type 2 regions, why does the g(x) or g(y) bound have to be the inner integral? Thanks!

Homework Statement Calculate the area under the curve for the following: f(x) = √x*√(−32 − x) and g(x) = √(−x2 − 32x) Homework Equations The Attempt at a Solution I've been trying to do partial integration since the functions f(x)=g(x)area are mirrored, so they are equal...

Find the volume of the finite region enclosed by the surfaces z = 0 and x2 + y2 + z = 1 I know I have to do triple integration on dV to accomplish this but do not know where to start and what limits to use for x, y and z? Cheers guys

I'm having some problems integrating fractions. If you could help me understand it, that would be great. Homework Statement \int\frac{2+3sin^{2}x}{5sin^{2}x}Homework Equations \int(x)dx=\frac{x^{n+1}}{n+1}The Attempt at a Solution...

Homework Statement \int\frac{x^{2}+2x+1}{x^{2}+1}Homework Equations INTEGRAL OF X=\frac{x^{n+1}}{n+1} I can't get the integral to work on the left side for some reason. The Attempt at a Solution I have completely forgotten how to integrate fractions. I know that "log(x^2+1)+C" would be...

Homework Statement The integral from v=vi to v of v^-2dv = -3 integral from t=0 to t of dt Homework Equations The Attempt at a Solution I am getting -1/v + C=-3t and the book is getting -1/v+1/vi=-3t. Not quite sure where they are getting 1/vi as I am getting C.

Hello I'm trying to solve the following DGL with an integrating factor: x'=xg(y) y'=yh(x) which is equivalent to -yh(x)dx+xg(x)dy=0 which is an inexact dg? How to i find an integrating factor in this case? thx

Homework Statement Integrate the function f(x,y,z)=−4x+3y over the solid given by the figure below, if P = (5,1,0) and Q = (-5,1,2). [PLAIN]http://img259.imageshack.us/img259/958/sfig1681g1.gif Homework Equations x=rcos(\theta) y=rsin(\theta) r=sqrt(x^2+y^2)The Attempt at a Solution i...

I am currently facing a problem of integrating exp(-ax^2)*erf(bx+c)*erf(dx+f) with the integral boundaries 0 and infinity. I have gone through some handbooks but what I could locate is the integration of exp(-ax^2)*erf(bx)*erf(cx) from 0 to infinity which yields...

Homework Statement Given two vector fields: i) A \frac{\vec{r}}{r^{n_{1}}} ii) Ae_{z} \times \frac{\vec{r}}{r^{n_{2}}} where A is a constant and n_{1} \neq 3 and n_{2} \neq 2 find \int \vec{F} dS through surface of a sphere of radius R Homework Equations \int \vec{F} r^{2}...

Homework Statement Integrate. \int e^{2\theta}sin(9\theta) d\theta Homework Equations Integration by Parts \int udv = uv - \int vduThe Attempt at a Solution I started out with integration by parts (IPB). u = e^{2\theta} du = 2e^{2\theta} d\theta v = \frac{-1}{9}cos(9\theta) dv =...

Integrating tan^5(x)... [UNSOLVED] Homework Statement \int tan^5(x) dx Homework Equations tan^2(x) = sec^2(x) - 1 The Attempt at a Solution First I split it up into (3+2). \int tan^3(x)tan^2(x) dx Using the identity for tangent squared... \int tan^3(x)(sec^2(x) - 1) dx...

Homework Statement I have a set of data points, and I need to find the area under the curve they form. I am trying to use Maple for this, by using the PolynomialInterpolation() to fit a curve to my list of points. I then would just integrate this function over the appropriate interval...

Homework Statement ∫√(2+cos3(t)) dtI should perhaps have tried to get the lower and upper limits of this integral (it's defined), but all I'm wondering about is how to calculate the integral. I don't need the answer, but if someone could just point me in the right direction. I've tried...

Hallo there. I m trying to integrate a bessel function but with no great success... I thing it can't be calculated.. I m trying to simulate the airy pattern of a certain aperture radius and wavelength in matlab. the integral is : int (besselj(1,16981.9*sin(x)))^2/ sin(x) dx where you can...

Homework Statement Not specifically a homework assignment, but for a personal project - but it's almost entirely parallel with my Physics course at the moment, and is mostly a homework-style question! I have an object acclerating due to a force, experiencing friction. Both the accelerating...

First let me write out the definition of a manifold given in my book: Let k > 0 . A k-manifold in \mathbb{R}^n of class C^r is a subspace M of \mathbb{R}^n having the following property: For each p \in M , there is an open set V \subset M containing p , a set U that is open in...

I couldn't figure out how (*) derived. How can the underlined part's sine function vanishes? http://img149.imageshack.us/img149/8642/asfdg.png Uploaded with ImageShack.us

Homework Statement Integrate Homework Equations integrating following equation about dx: (b1-(b1*x/L)+(b2*x/L))^2 The Attempt at a Solution I expanded all terms than integrated. I used integration by part to get it down to this but I am curious to see if there's better way to...

Homework Statement Solve the differential equation with the initial condition y(0) = 1 Homework Equations 3e5xdy/dx = -25x/y2 The Attempt at a Solution First I tried putting everything with an x or dx on one side and a y or dy on the other side, and solved for C. I got 0 as the...

Homework Statement Write a script file to integrate the function f(x)=x^3+tan(x)+C using the trapezium rule.Calculate the integral between the end points x=2 and x=4 with strip size 0.1.Calculate the integral for range of values from 1 to 3 in steps of 0.1.plot the integral obtained for...

Not sure if this question belongs more here or in Topology & Geometry or in Math & Science Software... I'm trying out the technique described in Bachman: A Geometric Approach to Differential forms, § 6.2 "Integrating 2-forms". To take a simple example, I tried to use this method to get the...

Ok so I'm doing my online homework and I came across this problem: "Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=11, y=x+28/x about x=-4" So I attempted to...

Hi I have an integral as follows, int((1/x)exp(-x),x,0,s) I want to integrate from [0,s). My question is how to integrate without including s as the upper bound. Any help will be appreciated

Hello everyone, This is my first post on the forum; I'm pretty sure my question fits in this section. I am having a lot of difficulty finding the definite integral \int^{+\infty}_{-\infty}e^{-2ax^{2}} dx where a is positive and real. I know the answer is [tex]\\sqrt{\frac{\pi}{2a}}, but...