Integrating Definition and 971 Threads

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...

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...

Homework Statement Integrating 1/xlnx by parts... Homework Equations Find the integral of 1/xlnx The question asks to solve by substitution, which I can do and results in ln(ln(x)) + c It then asks to compute using integration by parts, and then to explain how it can be true (because...

Hello all! :smile: I through a section in my text (by https://www.amazon.com/dp/0133214311/?tag=pfamazon01-20) on 1st Order linear ODEs. I am understanding the derivation of the integrating factor method pretty well; however, there are some aspects of the mathematics that I am getting hung up...

\int \frac{\sin x}{x }dx

Homework Statement t seconds after the brakes of a car are put on, the acceleration of the car is a(t) = -6t - 4 ft/sec^2. If the automobile was moving at the speed of 32 ft/sec when the brakes were put on, how far does it go before stopping? Homework Equations a(t) = -6t - 4 ft/sec^2...

It seems to me that integrating a polar equation should give you the arc length of the curve, rather than the area under it. This is my reasoning: A polar equation is in the form of: (1) r = f(\theta) The arc length of a segment of a circle where the radius is constant is given...

Homework Statement The acceleration of a certain particle is a function of time: a(t) = pt2-qt3, where p and q are constants. Initially, the velocity and position of the particle are zero. (a) What is the velocity as a function of time? (b) What is the position as a function of time? The...

Homework Statement integrate: sin (2x)/(1+sinx) Homework Equations (sin x)^2 + (cos x) ^2 = 1 sin (2x) = 2 sin x cos x cos (2x) = (cos x)^2 - (sin x)^2 The Attempt at a Solution I've been trying to integrate this thing for about an hour by rearranging various trig...

Homework Statement I haven't done much math for years. just a little reminder would be very appreciated. when you take integral for (2x^2+1)/x dx I believe this can break down into integral 2x dx + integral 1/x dx What I wondered about was is this summation of those two as...

Homework Statement Starting from the modified Newton's Law (dp(rel))/dt=F with a constant Force F, and assuming that the particle starts with v=0 at time t=0, show that the velocity at time t is given by V(t)=c [(Ft/mc)/(1+ Ft/mc)] Homework Equations The Attempt at a...

Homework Statement This is the problem I was given: I_{n} = \int^{0}_{\infty}(1 + x^{2})^{-n} dx I was told to "deduce that" I_{n} = 2n(I_{n} - I_{n + 1}) so I can "Hence or otherwise show that" \int^{0}_{\infty}(1 + x^{2})^{-4} dx = \frac{5\pi}{32} Homework Equations I...

hey guys I am absolutely stumped on this one integration problem: it asks us to integrate sin (2x) e ^ (sin x) i integrated by parts once and was left with an even larger term to integrate, which leads me to believe that i might be doing it wrong any help is appreciated, thanks

Homework Statement See figure Homework Equations The Attempt at a Solution For an integral like this am I allowed to evaluate the cross product between the to vectors, \vec{u} and \vec{v}? If so then, \vec{p} = \vec{u}\times\vec{v} and, \int f\vec{p} = -3\int...

Homework Statement How to integral this one? 1/(1+a*cosx) Homework Equations The Attempt at a Solution

Dear all, How can I derive the volume of a spherical cap by integration and using the Cartesian coordinate system. The sphere is located at the (0,0,0) coordinates and its radius is set to r. The height of the cap is also set to (r-h). I googled a lot but I couldn't find it. I would...

Homework Statement I was looking at the book's example. The author left the final integration as an exercise, and I was attempting it. 1/2 integral of [ (2 - 2sin(delta) )^2 - 0 ] d delta from 0 to 2pi for the sake of work, i will let x = delta (2-2sin(x))^2 => 4 - 8sinx + 4sin^2(x) and i...

Geometrically: Is it correct of think that a line integration in effect converts a curvilinear segment into an equivalent straight line?? If this is basically applicable then it would mean converting the accelerating worldline into a straght line in Minkowski space. My...

Hi, I want to do the following calculation: c_{m,n} = \int_{-\infty}^{\infty} t^m \phi(t-n)\,dt I know three things: I know the values of c_{m,n} for m={0,1} and the first 4 for m={2,3} I know that my \phi is symmetric, i.e. \phi(t) = \phi(-t) The Fourier transform of \phi(t)...

Hi everyone! I'm trying to work with an accelerometer to measure distances (straight line) but I'm not being very successful.. I've made this experiment: attached the accelerometer to a electric slot car and accelerate it to the maximum until it reached the end of a straight line track...

First order nonlinear ODE -- Integrating factor + exact differentials, or not? Hello everyone, (I apologize if this did not format properly, if not I will attempt to edit it if that functionality is available upon submitting a question). I recently came across the following nonlinear ODE...

Homework Statement Find the average value of z for a the spherical surface of radius R that resides above the x-y plane. Homework Equations Equation of a sphere x^2+y^2+z^2 = R^2 The Attempt at a Solution I rearrange the equation above and do a double integral z_{total} = \int...

Hi all, I have an exceptionally basic question, taken from P21 of Zee. Eq. 14 is Z=\int D\psi e^{i\int d^4x(\frac{1}{2}[(\partial\psi )^2-m^2\psi^2] + J\psi)} The statement is then made that 'Integrating by parts under the \int d^4x' leads to Eq. 15: Z=\int D\psi e^{i\int...

Homework Statement I need help in finding the answer of this integration: \int \frac{d^n [(x^2-1)^n]}{dx^n}dx I have no idea how to even start, please at least give me hints how to substitude. Thanks Alan

Homework Statement Solve the inital value problem for y(x); xy′ + 7y = 2x^3 with the initial condition: y(1) = 18. y(x) = ? Homework Equations dy/dx +P(x)y=Q(x), integrating factor=e^∫P(x) dx The Attempt at a Solution Multiplied all terms by 1/x to get it in correct form...

Hi I have a question, if I have a function that is continuous on the interval [a, b] where a <= b, why would integrating this interval backwards (i.e. taking the definite integral from b to a) be the negative of taking the definite integral from a to b? Can someone explain this from the...

Homework Statement For positive integers m and n, calculate the two integrals: \frac{1}{L}\int^{L}_{-L}sin(\frac{n \pi x}{L})sin(\frac{m \pi x}{L})dx and \frac{1}{L}\int^{L}_{-L}sin(\frac{n \pi x}{L})cos(\frac{m \pi x}{L})dxHomework Equations \int u v' dx = [u v] - \int u' v dxThe Attempt at a...

Homework Statement Solve (x + 2) sin y dx + x cos y dy = 0 by finding an integrating factor .....M......N..... M_y (x+2)siny = (x+2)cosy N_x xcosy = cos y M_y not equal to N_x, therefore equation is not exact.. so far so good? thanks Homework Equations The Attempt at...

Verifying an integrating factor --please check my work , thanks. Homework Statement Verify that 1/y^4 is an integrating factor for (3x^2-y^2)dy/dx - 2xy = 0, and then use it to solve the equation (1/y^4)* (3x^2-y^2)dy/dx = 2xy* (1/y^4) =3x^2 / y^4 dy = 2x/y^3 dx =3x^2 / y dy = 2x...

Homework Statement Let A be the region that in space bounded by the balls: x^2 +y^2 + z^2 =1 , x^2 +y^2 +z^2 =4 , above the plane z=0 and inside the cone z^2 = x^2 +y^2 . A. Write the integral \int \int \int_{A} f(x,y,z) dxdydz in the form: \int \int_{E} (\int_{g^1(x,y)}^{g^2(x,y)}...

Hi alll, I have an integral which includes a Kronecker delta: I = \int_{u=0}^{a} \int_{v=0}^{a} F(u) G(v) \delta_{u,v} \, \mathrm{d}u \, \mathrm{d}v I know that for a 1D integral there exists the special property: \int F(u) DiracDelta(u-a) = F(a) However, is there something equivalent for...

Homework Statement 1 ⌠ | 10^(1/2)*(x^5)+(5*x^(1/5)) | dx ⌡ −1 Homework Equations once the absolute value is gone you can just integrate the function The Attempt at a Solution how do you get rid of the absolute, and how do you then integrate it, do you use the product rule...

Homework Statement find \int\int_D sin\left(\frac{y}{x}\right)dA bounded by x=0, y=\pi, x=y^2The Attempt at a Solution I've only studied calculus 1, this problem is for my friend. I did read up briefly on double integrals however and this is why I'm stuck: From the limits and where the graphs...