Integrating Definition and 940 Threads

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...

I have been looking for problems to work out for practice and came across one I have no idea how to even start about. Say a box is dropped from a plane, with a parachute attached to it. If we are given two equations for velocity in terms of time, such as Vx(t)=Vo cos(θ) e^(-pt) and...

Homework Statement Integrating X^3/((e^x)-1), where we integrate from -infinity to infinity The Attempt at a Solution We thought about it, and we're not entirely sure if integration by parts is applicable here. Is there a table with this function perhaps?

Homework Statement integrating a circle ,, my main question is that, can we integrate it by contour integration technique ? and if yes ,, would you please show me how :) or just give me a hint :D Thanks is advance :-) Homework Equations y^2 + x^2 = a^2 where a= r suppose...

Homework Statement Specifically what i don't understand is a situation where you can't get the equation in the standard form of y' + p(x)y = q(x) the integrating factor is e^integ p(x), but what if y is part of a sin or cos, as in this equation: (x+2)sin y dx + xcos y dy = 0 if i...

question: Consider the gaussian distribution: p(x) = Ae^(-\lambda (x-a)^2) (a) use the equation, 1={\int_{-\infty}^{\infty}} p(x)dx (b) find <x>, <x^2> and \sigma ------------------------------------------------------ a) if i take (x-a) to be u, 1=\int_{-\infty}^\infty...

Homework Statement The question asks that you prove that \int\frac{sin^{2}x}{x^2}dx = \pi / 2 The integral is from zero to infinity, but I don't know how to add those in latex. Homework Equations Use a contour integral to get around the pole at z = 0. The problem is, I'm really really foggy...

Homework Statement my integrating factor for the DE ty' + (t+1)y = t is mu(x) = e^integ (1+(1/t)) = e^(t + ln|t| + c) so does this simplify to this...or not? = e^t + t + c so that DE becomes: ((e^t) + t))y = (e^t) + t) and then after integrating... ((e^t) + t))y = e^t +...

Orthonormal basis \big(\frac{1}{\sqrt{2}}, cos(2x)\big) \pi \int_{-\pi}^{\pi} sin^4(x)dx=\frac{3\pi}{4} Solve the integral without integrating. sin^4(x)=\big[\frac{1-cos(2x)}{2}\big]^2=\frac{1}{4} - \frac{2cos(2x)}{4} + \frac{cos^2(2x)}{4} I know I could rewrite cos^2(2x) but then I...

Homework Statement Solve: (1-\frac{x}{y})dx + (2xy + \frac{x}{y} + \frac{x^2}{y^2})dy = 0 The Attempt at a Solution No idea what strategy to use here. Tried using an integrating factor, but no success. A lot of x/y in here makes me think I need to use a substitution, but there's also...

Homework Statement solve the following initial condition problem x (d/dx) y(x) + 4xy(x) = -8-y(x) y(4)=-6 Homework Equations The Attempt at a Solution first i rearranged xy'+y+4xy=-8 xy'+y(1+4x)=-8 y'+y(1/x+4)=-8/x integrating factor:e^\int(1/x+4) e^(lnx+4x) x+e^4x multiplying...

y' + y = e^x ; y(0) = 1 1st, i calculate the integrating factor... u(x) = e^x times the integrating factor with DE... y'e^x + ye^x = e^2x dy/dx e^x + ye^x = e^2x d/dx ye^x = e^2x ye^x = ∫ e^2x dx ...= 1/2 e^2x + C y = 1/2 e^x + C the problem here, i didn't get the...

Question: (1 - x - z)dx + dz = 0 let M = (1 - x - z) ; N = 1 dM/dz = -x ; dN/dx = 0 hence, not exact. integrating factor... 1/N[ dM/dz - dN/dx ] = 1[-x] .......= -x e^∫-x dx = e ^ [(-x^2)/2] times integrating factor with DE.. {e ^ [(-x^2)/2] -x e ^ [(-x^2)/2] - z e ^...

y dx + x ln x dy = 0 ; x > 0 my integrating factor is x.. so.. multiply with DE, xy dx + x^2 ln x dy = 0 let M = xy ; N = x^2 ln x dM/dy = x ; dN/dx = x + 2x ln x the problem is.. i didn't get the exact equation after multiply the integrating factor.. I've double...

Homework Statement Show that given function μ is an integrating factor and solve the differential equation.. y^2 dx + (1 + xy) dy = 0 ; μ(x) = e^xy The Attempt at a Solution let M = y^2 N = (1 + xy) dM/dy = 2y dN/dx = y hence, not exact equation. times μ(x) = e^xy to the...

Hey guys working on a problem for an assignment but my algebra is weak regrettably and I need some assistance. Note:: I left the x and dx out for clarity. Homework Statement int csc/cot2 The Attempt at a Solution int csc x/cot2x dx= int csc/cos2/sin2 = int cscsin2/cos2 = int...

Hello, Just wondering if someone can help me make sense of something. I realize it's probably a simple problem, but my math skills aren't the best and I can't see through it. I'm trying to end up with this kinematic equation: X= Xo + Vo(t-to) + 1/2(a)(t-to)^2 And to do this the...

hello, I'm new to the forums. Can someone help me with integrating kinematics problems? For example velocity= Be^(-rt), where B= 3.00 m/s and r=0.500 s^-1. i don't understand how the integral's unit becomes m (since the integral of velocity is displacement). someone help me! thanks

Homework Statement \int dx/(e^{x}\sqrt{1-e^{-2x}}) Homework Equations The Attempt at a Solution I have absolutely no idea of how to start the problem, any help is greatly appreciated! thanks!

When we integrate a function f(t) with respect to t, we are finding the area under the curve f. Intuitively, this is very clear. What is the intuition behind integrating a function with respect to another function? ex. \int f(t)dg where g is itself a function of t?