What is Integrate: Definition and 650 Discussions

As you can see the function given is K/[(y2 + K)1.5] The integral of this equation with respect to dy is part of the explanation my textbook gives of finding electric field due to line of uniformly charged wire, where y of course is the variable length of the wire. Then it gives the integral...

Evaluate the integral over the contour C when: f(z) = 1/z and C = {z(t) = sin(t) + icos(t) | 0 <= t <= 2*pi} I know f(z) = 1/r*e^(-it) = 1/r(cos(t) + isin(t)). But, when I try to take the contour integral by integrating f[z(t)]*z'(t), I get really messy formulas ((1/r*cos(sin(t))...

Hey guys! I have absolutely no experience with integrals, but i find them interesting. I do know that they represent the area between the function and the x-axis, but not much else. I was wondering if anyone could give me a simple explanation of what an integral is and how to actually solve one...

Can anyone show me how to do this: \int_a^b \left[\frac {\sin x}{x}\right]^2 dx

Homework Statement How do you integrate S x/(x-1) dx Homework Equations IBP The Attempt at a Solution I tried using Integration by Parts with u= x/(x-1) and dv = dx and that did not work out. Then I tried using u= 1/(x-1) and dv = xdx but that did not work either. A google...

Can you please tell me how to integrate by parts the d'alembertian of a 4-variable function over a volume dx * dy * dz * dt. I have stumbled upon this seemnigly simple exercise on my way to understanding QFT of scalar fields.

Homework Statement Evaluate the following integral by first reversing the order of integration ZZR x^3 e^(y^3) dxdy The first integral is from 3 to 0 and the inner integral is from 9 to x^2 Homework Equations The Attempt at a Solution i know how to revers the order its just...

Hello! I'm trying to calculate this integral: Integrate [Exp[-I a *y] Exp[I*Sin[y]] Exp[-y*Sign[y]], {y, -Infinity, Infinity}] , where "a" - constant that i'll define later. So the result of the calculation acсording to Mathematica is the same expression : Exp[-I a *y] Exp[I*Sin[y]]...

Homework Statement I know the current distribution through a rectangular cross section of metal. It varies only with respect to y. I need to find a heating function for the metal. (This is only the relevant part of a larger problem). Homework Equations Q=I2R The Attempt at a Solution I...

Homework Statement Evalute the integral ∫ [x / 1 + x] dx Homework Equations ∫ [x / 1 + x] dx The Attempt at a Solution I forgot how to do solve this type of integral, or never had enough practice. And this problem is actually for a physics problem :-) And my algebra is very...

Homework Statement \int e^x \frac{1 + sin(x)}{1 + cos(x)}\;dx The Attempt at a Solution Apparently there is a trick involving e^x integrals like this \int e^x[f(x) + f'(x)] dx = e^x f(x) + C Now my question is not how to compute the integral above but where did this \int...

Homework Statement how does one integrate (1-a-cos x)-1/2, where a is an arbitrary constant? Homework Equations as above The Attempt at a Solution Thought of writing cos x as 1-2*(sin(\frac{x}{2}))2 then the integrand simplifies to [2*(sin(\frac{x}{2}))2 - a]-1/2... But then...

Hey guys, I recently did a project with combining and accelerometer and gyroscope together using the 6DOF IMU Razor and an Arduino and now i need to try something different but i need some help. How does one integrate a gyroscope output? I tried something like this below but i don't think...

Homework Statement How do you integrate: 1/3(x^2(50 - x^2)^(3/2)) Homework Equations The Attempt at a Solution I tried by parts with no luck :(

Integrate using partial fractions (arctan x) / ((x+1)(x^2+1))? My attempt: (arctan x) / ((x+1)(x^2+1)) = A/(x+1) + (Bx+C)/(x^2+1) arctan x = A(x^2+1) + (Bx+C)(x+1) when x= -1, A= -pi/8 so plugging in -pi/8 for B makes: x= tan[ (B-(pi/8))x^2 + (B+C)x + (C-(pi/8)) ] and when x=0, C=...

I noticed that in this case this is the answer: http://img804.imageshack.us/img804/3513/1con.jpg But this is what I turned up with: http://img163.imageshack.us/img163/4083/reupp.jpg And you can add a +c to that. What did I do wrong?

Why are they called "differentiate" & "integrate"? I was wondering why. When we differentiate, don't we result in an equation that describes the slopes of many other equations ( + C ) ? So, we'd be "integrating" many equations, different from each other by C, into a single description...

Homework Statement I need to integrate ∫ -y3ey2/2 Homework Equations Integration by parts The Attempt at a Solution I have tried several times, I am unable to find the correct solution, which is: -yey2/2 + 2ey2/2 + c

Homework Statement The graph in the attached file is a velocity-time graph. We have to find the total displacement from t=0 to t=10. I know that integration will be used for this problem, and i know my formulas but i do not know of how to form the equation of the two parabolas here. I...

Homework Statement integrate ln(cube root (2+y^3)) dydx with limits of y =sqrt (x) to 1 of x from 1 to 0 Homework Equations integral of ln x= x ln x. This ends up being very convoluted, haven't even begun to insert limits The Attempt at a Solution

dCb/dt = k1Ca-k2Cb dCb/(k1Ca-k2Cb)=dt Now integrate. ln(k1Ca-k2Cb)=t (k1Ca-k2Cb) = et Rearranging k2Cb=-et +k1Ca Cb= -et +k1Ca/k2

Homework Statement I have to find the antiderivative of 4/(1+2x)² New question: Find s(t) 2. Given variables and equations a(t) = 4/(1+2x)² v(0) = 0 s(0) = 5 The Attempt at a Solution ∫4(1+2x)-2 = 4∫(1+2x)-2 = 4[(1+2x)-1/-1] = -4/(1+2x) But the correct answer has a -2...

Homework Statement I want to integrate the 2-form defined on R^3\{0,0,0} over the unit sphere. (x/r^3)dy wedge dz+(y/r^3)dz wedge dx+(z/r^3)dx wedge dy Homework Equations r=\sqrt{x^2+y^2+z^2} The Attempt at a SolutionI'm thinking this is like a surface integral but I'm not really...

Hi. Is it possible to calculate the antiderivative of \frac{1}{Ax+B} if A and B are matrices? If they were scalars the result would be 1/A \log(Ax+B).

Which method do you use in integrating \int\((1-\beta^{2})sin(\varphi)d\varphi/(1-\beta^{2}(sin(\varphi)^{2})^{3/2} This integral is from Berkeley Physics Course Volume 2. Thanks in advance.

?Do you have to integrate velocity (v) to get the position function r(t)? Homework Statement http://img94.imageshack.us/img94/238/2010b5e.png Homework EquationsThe Attempt at a Solution attempted solution to first question below, don't know what to do for second...

how would you integrate (1+x^30)/(1+x^60) from 0 to 1? tried so many ways but in vain.. any help?

How would you integrate product of heaviside function and function of x i.e. int[f(x)H(x)dx] Thanks

Dears, Please help hem in order to resolve this problem. I estimated an power spectral density using welch method with Matlab program (Pxx). Now, I want apply this integration m[n] := Integral from f=0.0001 to f=0.001 over S(f) * f ^ n . In my case I think that m[n] := Integral...

Homework Statement \int \delta(t)^{2} dt from -infinity to +infinty Homework Equations \int^{\infty}_{-\infty}\delta(t)dt = 1 \int uv dt = u\int v dt - \int u^{'}(t)\int v dt dt \int^{b}_{a} f(x) dx = F(b) - F(a) \delta(-\infty) = \delta(\infty) = 0 The Attempt at a...

Homework Statement I'm having major issues working out how to integrate \int\frac{1}{F-Gx+x^{2}}dx , where F and G are constants. Homework Equations The Attempt at a Solution Maple tells me it is an inverse hyperbolic tangent of some description, and I know I have to...

Homework Statement \int\sqrt{sinx}*cos^3x Homework Equations The Attempt at a Solution by writing as root(sinx) (1-sin^2(x)) (cosx) i can solve but since the worksheet is called basic techniques of integration i am looking for an easier and more obvious solution if possible...

Homework Statement integrate 3^(log(base4)x) Homework Equations The Attempt at a Solution i tried to write it in different ways. couldn't solve. i tried to divide the whole thing by ln3 and then add some more constants to cancel out the remainings. still i could not cancel out the x in the...

Homework Statement We're trying to integrate a vector, E, with components, Ex = 6x^2y, Ey = 2x^3 + 2y and Ez = 0, from the origin to x = -0.4, y = 6.1, z = 0.0. Homework Equations integral E dot dr = V The Attempt at a Solution i don't know how

Can Someone explain Why we integrate over 4\pi? What allows us to get rid of Omega?

I'm having trouble with integrating this. \int_1^8 \sqrt{9x^{4}+\frac{1}{2}+\frac{1}{144x^{4}}} dx I can get the problem down to \int_1^8 9x^{2}+\frac{1}{\sqrt{2}}+\frac{1}{144x^{2}}} dx , but I don't know how to integrate the last two terms in that integral. Am I doing something wrong?

I am familiar with integration, but I'm stumped with this. How do you integrate something such as \int(from 0 to 2)\sqrt{65e(to the power of 2t}dt That is supposed to be the square root of 65e to the power of 2t.

Homework Statement Perform the following integration: \int_{0}^{\sqrt{2}h}\frac{x}{\sqrt{h^2+x^2-\sqrt{2}hx}}dx Homework Equations The solution (via wolframalpha.com) is: [\sqrt{h^2+x^2-\sqrt{2}hx}+\frac{h}{\sqrt{2}}ln(2(\sqrt{h^2+x^2-\sqrt{2}hx}+x)-\sqrt{2}h) Evaluated from 0 to sqrt(2)h...

[b]1. Integral of (x^4)/(1-x^2)^(3/2) dx i let x=sint so dx=costdt used the right triangle and simplified to integral of ((sint)^4)/((cost)^2) dt

Hi, Part of solving a differential equation involves integrating M(x,y) with respect to x, where M(x,y) = x + tan-1(y). What are the steps to integrating the arctan portion? \int tan-1(y) dx Thank you.

Homework Statement let u=lnx du=1/x*dx dv=cosdx v=-sin Homework Equations Now I am confused as I am getting nowhere with this substiution, i learned the LIPTE rule but its quite confusing, i have a function within a functionThe Attempt at a Solution

Homework Statement at= 0.5etm/s2 Homework Equations at = dv/dt The Attempt at a Solutionv = integration of 0.5et

Homework Statement dy/dx=a^2/(x+y)^2 where a is a constant need the answer in the form x=f(y) Homework Equations The Attempt at a Solution multiplying out (x+y)^2 gives dy/dx=a^2/(x^2+2xy+y^2) setting u=y/x dy/dx can be rewritten as dy/dx=a^2/((x^2)*(u+1)^2)...

Homework Statement dy/dx=a^2/((x+y)^2) where a is a constant express answer in the form x=f(y) Homework Equations The Attempt at a Solution let u=x+y du/dx=1+dy/dx du/dx=1+(a^2)/(u^2) int(du/(((a^2)/(u^2))+1))=int(a^2 dx) after integration substituting back in for u...

Homework Statement Well gentlemen, another year, another integral eh? Anyways, \int \frac{1}{x^4+4}\,dx I really want to do this without looking at Wolfram/Google. Homework Equations U-substitutions, parts, partial fractions The Attempt at a Solution Basically I tried to...

Homework Statement Integrate Exp[-(y^2)]*(y^2) w.r.t. y Homework Equations The Attempt at a Solution i need to express the answer in terms of error function Error Function: Erf(x) = 2/Sqrt[Pi] *Integrate Exp[-t^2] w.r.t. t, from 0 to x My attemp is to use integration by part, seems...

I am trying to do this integral \int_{-\infty}^{\infty}\frac{e^{-a| \vec{r}|}e^{-\vec{b}. \vec{r}}}{|\vec{r}|} But if I write the modulus as \vec{r}=\sqrt{x^{2}+y^{2}+z^{2}} I can't figure out how to handle the annoying square root in the exponential. Would be grateful for hints, thanks...

how integrate x^x^x ?my teacher ask me)what do you think about it?

the question: integrate y= arctanx for 0< x <1 i know to solve this question you should use the method of integral by parts, so i tried doing that and at some point i got x arctanx - integral of x/1+x^2 (between 0 and 1) .. from this point on i tried using the substitution method, w = 1...

can someone explain what happened after the part where it says "= warcsinw - integral of w/sqrt(1-w^2) = ... " ? i don't see how they got sqrt(1-w^2) + C