Integrating Definition and 971 Threads

Can anybody recommend a good site to bone up on differentiating and integrating ln and e functions?

Homework Statement \int\frac{\sqrt{x^{2}+1}}{x^{2}} dx Homework Equations The Attempt at a Solution I tried a Trig Substitution with x=tan(u) and ended up with \int (csc(u))^{2} * sec(u) du From here I am kind of stuck. I tried a few different integration by parts methods, but they got...

Homework Statement A solid "rough" of constant density (\delta =1) is bounded below by the surface z=4y^2,above by the plane z=4, and one the ends by the planes x=1 and x=-1. Find the center of mass...Homework Equations _{M}xy =\int\int\int z \delta dV Mass = \int\int\int\deltadV then to find...

Q: Given that G(x,y,z)=(6xz+x3, 3x2y+y2, 4x+2yz-3z2). Find F such that curl F = G. Solution: ... A particular solution is Fo=(-3x2yz-y2z, 2x2-3xz3-x3z) And then my textbook says that the general solution is F=Fo + grad f where f is an arbitrary C1 function...

Homework Statement Finding the area of a disc by integration of rings. Homework Equations A ring of radius r and thickness dr has an area of 2 \pi rdr. The Attempt at a Solution Why isn't it \pi (2rdr + (dr)^2)?

This integral came up while trying to find the potential of a uniformly charged rectangle. \int \log(\sqrt{a^2+x^2} + b) dx Integrator gives a pretty long expression involving inverse tangents so I'm not sure where to begin at all. I tried integrating by parts once, taking u to be the...

how do you integrate \frac{dy}{dx}=4x-2y. I don't know if this is right, but this is where I'm going with this: y'=4x-2y y'+2y=4x Solving homogeneous for complementary solution: y'+2y=0 Solving auxiliary equation: m+2=0 m=-2 Which gives y=c_{1}e^{-2x} y'=-2c_{1}e^{-2x}Now solving original...

Homework Statement \int tan^5(6x) sec^3(6x) dx Homework Equations The Attempt at a Solution first off I set u=6x to get 1/6\int tan^5(u) sec^3(u) dx then I used trig identities to put tangent in terms of secant and I came up with \int...

Homework Statement I would like to prove that {d \over {dx}} \sigma(x)=2\delta(x), where \sigma(x>0)=1 \sigma(x=0)=0 \sigma(x<0)=-1 Homework Equations The Attempt at a Solution I think that I need to show that \int_{-\infty}^{\infty}{d \over {dx}}...

[SOLVED] Integrating factors or separating the variables Homework Statement The following equation can be solved by intergrating factors or by separating the variables. \frac{dy}{dx} - \frac{y}{4x} = 0 with the initial condition of y(2)=3 Homework Equations The Attempt at a...

[SOLVED] Integrating Factor Diff Eqs Homework Statement g ' - g/t = t e^t I'm trying to solve this, but I seem to have run into a problem, according to my book the integrating factor is 1/t, however I believe that it is -t Homework Equations The Attempt at a Solution...

Homework Statement I need help integrating: mg/b(1 - e^(-bt/m) The Attempt at a Solution I came up with mgt/b - mg/b(-b/m * e^(-bt/m) It's been a while since calculus, can someone help me with this.

Homework Statement Use the substitution x=4sin(t) to evaluate the integral: S 1/[(16-x^2)^(3/2)] dxHomework Equations x = 4sin(t) The Attempt at a Solution x = 4sin(t) dx = 4cos(t) dt 4cos(t) = (16-x^2)^(1/2), i cube both sides to get (4cos(t))^3 = (16-x^2)^(3/2), then plug in dx and...

I am trying to evaluate the following integral. \int_{-\infty}^{\infty}{\delta(2t-3)\sin(\pi t) dt} where delta represents the Dirac delta function. I am told that the answer is -1. However, when I evaluate it in MATLAB and Maple 11, I get an answer of -1/2. What is the correct way...

I was trying my hand at integrals with 2 variables... So.. my first excercise was to find out the surface area of a sphere. So, the co-ordinate system is something like this: i] The whole co-ordinate system is mapped on the surface of a sphere. ii] The x-axis of the sphere is like the equator...

Homework Statement Not real good with the easy text stuff yet so ill give it a shot. definite integral of (1/(1+t^2))dt from 0 to x^2 then find the interval for which the curve is concave upward. I totally forgot how to integrate problems like this. It is some sort of substitution I...

how do i integrate 1/(x^2 +4)? please help

Homework Statement Integrate the following \int\sqrt{1-sin2x} dx Homework Equations sin2x=2cosxsinx cos2x= cos^2 (x) -sin^2 (x) The Attempt at a Solution I've rearranged the integral so its 1-sin2x/\sqrt{1-sin2x} but other than that I've just been randomly trying stuff. Any hints...

Integrate sqrt(1 +a^2*x^2) dx Thanks

Hi everyone. I was curious how I could integrate a matrix. Is it just as simple as separately integrating each of the entities of the matrix, or is it more complex than that?

[SOLVED] Integrating substitution problem? Homework Statement Sorry to hijack this thread sort of (as a similar named one already exists), but the title is aptly suited to my question. I have integral to integrete and I don't really know how to do it tbh. . . s=\int{\sqrt{2+(3t)^2}dt...

1. Homework Statement Integrate h(x,y)=yi - xj over the triangle with vertices (-2,0), (2,0), (0,2) tranversed counterclockwise 2. Homework Equations (1-t)a+tb 3. The Attempt at a Solution (1-t)(-2,0)+t(2,0)=(-2+4t,0) (1-t)(2,0)+t(0,2)=(2-2t,2t) (1-t)(0,2)+t(-2,0)=(-2t,2-2t) integral y-x...

the intergral of 1/3x either equals 1/3 ln 3x or 1/3 ln x - i don't know which one is correct though because can't you take the 1/3 out of the intergral and then you get 1/3 ln x - so confused - i should really know this...

Hi, I'm trying to integrate an expression I derived from multiplying the Fourier transform of two Lorentzians together. The expression is \int^{\infty}_{-\infty}{dt.e^{-|t + \tau +a| - |t-a|} How do you go about solving this? I tried splitting it up but you have two different values of t...

I am trying to integrate (sin(x))/x It's an indefinite integral I can't think of any tricks to work this out

Homework Statement Using the macluarin's expansion for sinx show that \int sinx dx=-cosx+cHomework Equations sinx=\sum_{n=0} ^\infty \frac{(-1)^nx^{2n+1}}{(2n+1)!} The Attempt at a Solution Well I can easily write out some of the series and just show that it is equal to -cosx but if I...

Homework Statement A. (1-sin^2x)/(cos^2x) dx Upper Limit = pi/4 Lower Limit = 0 B. (x-2)/(sqrt x) dx Upper Limit = 4 Lower Limit = 1 Homework Equations The Attempt at a Solution A. I am having trouble with this one. B. (x - 2)/(x^1/2) = (x^1/2 - 2x^-1/2) = 2/3x^3/2 -...

Hi, I am having some difficulties integrating the following expression.. \int\int\left(\frac{k}{\pi}\right)^2 \frac{1}{k^2+\omega'^2}\frac{1}{k^2+\omega^2}e^{-i\omega'\tau}e^{i\omega\tau}d\omega d\omega' I've tried by part but it doesn't look like it's going to give me the right answer...

Homework Statement (2sinx - 5e^x) The Attempt at a Solution is it just... -2cosx - 5e^x

What does it really mean to integrate over all possible fields in the Path integral formulation of quantum field theory,and how does such a formalism goes out to decribe field quanta? Another question is im new to Quantum field theory i was wondering whether i should stick to the old...

Quick integrating question...(part of a series question) Still studying for my exam... Came across this example and I don't know what the method is for integrating this type of problem? (I'm using it to do the integral test for series). How did they get rid of the x^3? thanks for the help :-)

Hello! I need to calculate \int_{-\infty}^{\infty} x^{2} e^{-\frac{|x|}{b} dx and I know the answer should involve \pi. I've tried splitting the integral for x and -x with limits from 0 to infty and -infinty to 0, which gives me the answer of 2b. But I don't think this is correct. Does...

Homework Statement I'm actually in the middle of a multivariable question, and I am stuck because I don't remember how to integrate sin(\phi)cos(\phi) . The Attempt at a Solution I have an understanding of the material, but I can't remember how to integrate this. Someone please refresh...

Okay so I am suposed to evaluate 2 of these: 1.) \int\sin^3(a\theta)d\theta the solution manual looks like it used a trig ID to do this. Why?? Doesn't \int\sin^3u du=\frac{1}{3}\cos^3u-(\cos u)+C ? So just use the u-sub u=a\theta \Rightarrow du/a=d\theta So it should just be...

Homework Statement \int {\frac{{dx}}{{\sqrt {x^2 - 2} \left( {x^2 - 1} \right)}}} Homework Equations \frac{d}{{dx}}\arctan (x)The Attempt at a Solution \frac{d}{{dx}}\arctan (x) seems to be part of it, I can't quite get much farther...

Hi, I'm learning differential equations, and although I understand the methods I have learned thus far, I often have trouble seeing what is the reasoning behind them. Take for example, the use of the integrating factor when solving first order linear ODE's. I understand how to use it, but...

Homework Statement \int \frac{dx}{(x+1)(x^2+1)(x^3+1)} The Attempt at a Solution I tried to solve it in 3 ways. 1)\frac{A}{(x+1)}+\frac{B}{(x^2+1)}+\frac{C}{(x^3+1)} 2)\frac{A}{(x+1)}+\frac{B+Dx}{(x^2+1)}+\frac{C+Ex}{(x^3+1)}...

Let a0, a1, a2, a3 be arbitrary real numbers, and let f(x) = a0 + a1*x + a2*x^2 + a3*x^3 Show that the approximating the integral \int f(x)dx[/tex] ( Couldn't figure out the bounds using latex but the integral is from pi to 42) with Simpson's rule yields the exact value of this integral...

[SOLVED] Integrating with Change of variables -method Homework Statement Solve by "Change of variables"-method ∫(dx)/(eˆx + eˆ(-x)) Homework Equations ∫f(x)dx=∫f(x(t))*x'(t)dt The Attempt at a Solution ∫(dx)/(eˆx + eˆ(-x))=∫(eˆx)/(1 + eˆ2x) t=eˆx x=ln...

Homework Statement \int4x^-3*ln(9x) Homework Equations \int u'*v = u*v - \int u*v' The Attempt at a Solution i know the answer is \frac{-2ln(9x)-1}{x^2} but i don't understand the step \int u*v' if any could help me...thanks

As usual I did this question I'm working on backwards, doing the section dealing with air friction first. Now realizing I must do the 'first part' and I think I am over thinking again. With no air resistance, I need the position of a trajectory from Newton's second law. I know gravity is the...

1. Solve the equation [sin(xy) + xycos(xy)]dx + [1 +x^{2}cos(xy)dy = 0 Homework Equations The Attempt at a Solution [sin(xy) + xycos(xy)]dx = M(x,y) [1 +x^{2}cos(xy)dy = N(x,y) dM/dy sin(xy) = xcos(xy) xycos(xy) = uv' + vu' = (xy)(-xsin(xy)) + (x)(cos(xy)) u = xy du = x...

[SOLVED] More help in integrating Homework Statement Find a,b,n such that a,b are rational and n is not an element of Z. a>0,b<0 \int_{0}^{1} \frac{3x}{\sqrt{1+6x-3x^2}} = \frac{\pi}{a^n} + b Homework Equations \int \frac{1}{\sqrt{A^2-X^2}} dx= \arcsin{\frac{X}{A}+K \int \frac{x}{R} =...

Homework Statement Given that mechanical equation of state for a paramagnetic substance is m=\left(\frac{DH}{T}\right) where D is a constant, H is the magnetic field, m is molar magnetization and the molar heat capacity c_{m} is constant, find entropy and enthalpy Homework Equations...

I need to find the integral of (1/(1+e^x)) dx. ...I don't think I can use u substitution, but well, I'm basically open to suggestions.

I have a set of measurements that form a plot in MATLAB. I just want MATLAB to integrate (ie. find the area) in a certain region of x values...is this possible? All the integration functions I've seen require a function file or some sort of function...

My own question, carried to a new thread as not to derail another:

i'm at a loss about how to do this type of integration. can some one show me how to evaluate the integral of (d^3)k exp[ik*(x1-x2)]/[(k^2+m^2)(2pi)^3], where "*" is the dot product between the 3 vector k and (x1-x2), which are both 3 vectors. this come from the energy equation used to get the...

Homework Statement Use the integrating factor to solve the first order differential equation dy/dx + (2/x)y = 1 - 2/x subject to the initial condition y(1) = 2The Attempt at a Solution I have the full answer (it's an example), but my lecturer is notorious for omitting steps, to my constant...

Homework Statement \int_0 ^\pi \sqrt{1-\sin^2 x} dx Homework Equations 1 - \sin^2 x = \cos^2 x The Attempt at a Solution I don't know how to treat this since cos changes sign half way across the integral. I know the answer should be 2 but I keep getting 0 every which way I try.