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...
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...
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
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...
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...
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
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
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...
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
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...
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