Hi,
I'm v rusty on my integration so was wondering could anyone give me some guidance on how to find the solution to the following integral
integral (1/x^2+80x+1600)dx between the limits x=80 and x=0
Any help is much appreciated!
Regards
Daniel
Homework Statement
My solution has two terms divided by a which is in error. I am a volunteer math coach to some junior college students and can't find my error in the problem. Its been a while since I earned my masters in electrical engineering.
The issue is the presencce of the variable...
If k is a constant, I know
\frac{d}{dx} \ln(x) = \frac{1}{x}
\frac{d}{dx} \ln(kx) = \frac{k}{kx} = \frac{1}{x}
However, what about \int\frac{1}{x}.
I've been taught to use \int\frac{1}{x} = \ln(x),
but wouldn't \int\frac{1}{x} = \ln(kx) work as well.
And if this is true, there are an...
The question is attached .
N/A
I tried to integrate it using cos^2x=t
But it didn't work . The numerator is killing me.
Euler's equations are not applicable here . Therefore they don't work here . Thus how to solve it ?
Homework Statement
Integrate: (e^(2t))(25sint+20cost)dt
Homework Equations
Integration by parts twice
The Attempt at a Solution
I don't know what to set for u and v.
I ended up wolfram alpha it but I want to know how to get there.
The solution is:
e^(2t)(14sint+3cost)=C
Homework Statement
How to integrate dv/dt=g-kv/m?
Homework Equations
This is ODE.
The Attempt at a Solution
dv/(g-(kv/m))=dt
Now what? I don't know how to integrate the left side.
Homework Statement
Integrate x*sqrt(1-x^2)+(1-x^2)/2 dx from 0 to 1.
Homework Equations
None.
The Attempt at a Solution
How do I simplify this and find the integral of this?
Homework Statement
How to integrate the double integral cos(x+y) dy dx from 0 to pi and from 0 to pi again.
Homework Equations
The answer is -4.
The Attempt at a Solution
Here's the work:
u=x+y
du=dy
cos(u)du=sin(x+y)
integral of [sin(x+y)] evaluate from 0 to pi dx from 0 to pi
integral of...
Homework Statement
http://s23.postimg.org/wsj9e91wb/IMG_1334.jpg[/B]
photo of the problem
g(x)=∫ƒ(t) dt from -5 to x
ƒ(t) = (0 if x < -5
5 if -5≤x<-1
-3 if -1≤≤x<3
0 if x≥3)
(a) g(-8) = 0
(b) g(-4) = 5
(c) g(0) = ?
(d) g(4) = ?
Homework Equations
∫ƒ(x) from...
Question:
A single conservative force acts on a 5.00-kg particle. The equation Fx = (2x + 4) N, where x is in
meters, describes this force. As the particle moves along the x-axis from x = 1.00 m to x = 5.00 m,
calculate (a) the work done by this force.
Work = Force * Distance.
(2*(5-1) +4) =...
Homework Statement
FIRST
##\int x^2 \ln x \ dx##
SECOND
##\int \frac{(x+1)^2}{x}dx##
THIRD
##\int \frac{x-2}{x+3}dx##
Homework Equations
N/A
The Attempt at a Solution
I tried using the integration by part method but it doesn't work.
For the FIRST problem:
Setting ##u=x^2## or ##u=\ln x##...
I don't understand the question:
"First make a substitution and then use integration by parts to evaluate the integral"
\int sin \sqrt{x} dx
What does it have in mind by "substitution"?
Homework Statement
Integrate e^(ax+by)(a*cos(xy)-y*sin(xy)) with respect to x.
Homework Equations
None.
The Attempt at a Solution
The answer is (cos(xy))(e^(ax+by)). I know that I need to treat y as a constant since I'm integrating it with respect to x but I don't know how to integrate this...
Homework Statement
How to integrate dz/(z^2+2z/x)?
Homework Equations
None.
The Attempt at a Solution
I did partial fractions but it doesn't seem to work.
A/z+B/(z+2/x)=1
Hello, I'm hoping somebody can give me some insight on how to solve this problem. This was a solid mechanics exam question and I wasn't able to finish it because I'm rather weak in math.
1. Homework Statement
Homework Equations
Recall divergence theorem for part ii. ∫div(V)dA = ∫V⋅ndS where...
Homework Statement
Let f(x1, x2, x3) = e-(x1+x2+x3), 0<x1,2,3<infinity, zero elsewhere be a joint pdf of X1, X2, X3. The variables are all independent to each other
Compute P(X1< X2< X3|X3<1 )
Homework Equations
P(X1< X2< X3|X3<1 )
The Attempt at a Solution
P(X1< X2< X3|X3<1 )=P(X1< X2< X3<1...
Homework Statement
I need to integrate x/sqrt(a^2+b^2-2abx) with respect to x.
The Attempt at a Solution
This follows from a substitution of the form x=cost in a textbook I'm reading - they jump to the solution straight from the above and I have no idea how to go about it - any hints will...
Hello!
I'm having some trouble determining, when trying to find the area between two curves, when to integrate with respect to y or respect to x, given two equations only?
Thanks!
Integrate[f[qs] DiracDelta'[qs (1 - 1/x)], {qs, -\[Infinity], \[Infinity]},
Assumptions -> 0 < x < 1]
Integrate[f[qs] DiracDelta'[qs - qs/x], {qs, -\[Infinity], \[Infinity]},
Assumptions -> 0 < x < 1]
This is on Mathematica 8 for windows.
The results differ by a sign. They are effective...
Hi All,
I am trying to understand the some of the properties of wakefields, namely the energy change. So, as a preface I am interested in primarily the wakefield due to electron beams as they progress through a curved section (the eletcrons radiate strongly when they are in circular motion)...
Homework Statement
How to integrate∫√(2+2sinθ)
Homework Equations
Making use of (2+2sinΘ)(2-sinΘ)=4-4sinΘ^2
The Attempt at a Solution
Multiply and dividing the integrand by √2-2sinΘ
Hello,
For a practical I have to know the work done by drag force, but drag force which is bv2 is not constant over the path, how can this be done, or should I just add every tiny bit of work, supposing Fd is constant over that tiny path. Thanks for the help!
∫x(x^{2}+1.44)^{-1/2}(dx)The only technique of integration I know of is to recognize the antiderivative (which I can do for this one but) I'm tired of being limited by antiderivatives.I was wondering how would you go about solving this?
Homework Statement
The c.d.f. of a random variable X is given by the following formula
F(x) = 1 - e-x2 x≥0
Find M(t). Moment generating function.
The Attempt at a Solution
I've found the pdf as
f(x) = F'(x) = 2xe-x2 x≥0
To determine M(t) I need to do the following...
I would like to know how do we solve d2x/dt2 = k' where k' is a constant i.e the task is to find x as a function of time ?
One way to approach this is to rewrite it as vdv/dx = k' where v=dx/dt and first find find v as a function of x and then rewrite v as dx/dt and then find x as a function...
Homework Statement
∫tan3x dx
2. The attempt at a solution
∫tan x + ∫tan2x
∫tan x (sec2x - 1) dx
∫(tan x (sec2x - tan x) dx
∫tan x sec2x dx - ∫tan x dx
u = sec x
du = sec x tan x dx
∫tan x sec x sec x - ∫tan x dx
Now I'm stuck..
∫ du * u - ∫ tan x dx ?
i'm trying to integrate this:
$$W=\frac{ε}{2}\int{\vec{∇}\cdot\vec{E})Vdτ}$$
where ε is a constant, E= -∇V, τ is a volume element
how do i end up with the following via integration by parts?
$$W=\frac{ε}{2}[-\int{\vec{E}\cdot(\vec{∇}V)dτ}+\oint{V\vec{E}\cdot d\vec{a}}$$]
where the vector a...
I'm trying to derive Saha's equation, and I've come up against this definite integral, which I can't seem to find anywhere and may not even be doable; I'm not sure.
\begin{equation}
\int\limits_0^\infty \frac{x^{2}}{e^{x}+1}dx
\end{equation}
Can anyone help? Thanks!
Homework Statement
Calculate ##\int _Kz^2exp(\frac{2}{z})dz## where ##K## is unit circle.Homework Equations
The Attempt at a Solution
Hmmm, I am having some troubles here. Here is how I tried:
In general ##\int _\gamma f(z)dz=2\pi i\sum_{k=1}^{n}I(\gamma,a_k)Res(f,a_k)## where in my case...
I'm trying to integrate the function Exp[-I*t*x - t^2/2] from -infinity to infinity using NIntegrate in Mathematica; the value that I get is accurate when x is small, but as x gets larger, the output from NIntegrate does not match the value I get when I use Integrate -- it gets less and less...
Homework Statement
Numerically integrate and plot the response of an underdamped system determined by m= 100 kg,
k= 20,000 N/m, and c = 200 kg/s, subject to the initial conditions of x0 = 0.01 m and v0 = 0.1 m/s, and the applied force F(t)=150cos(5t). Then plot the exact response.
Homework...
Hey! :o
I have the following exercise:
Integrate the function $f=x+ \sqrt{y} -z^2$ at the path from $(0,0,0)$ to$(1,1,1)$ that consists of the curves $C_1:r(t)=t \hat{ \imath}+t^2\hat{ \jmath}, 0 \leq t \leq 1$ and $C_2: r(t)=\hat{ \imath}+\hat{ \jmath}+t \hat{k}, 0\leq t \leq1$.My solution is...
Here is the code, I am using Mathematica 7 with no packages installed at the moment.
$Assumptions = 0 < u <= 19/80 && I10 \[Element] Reals;
FXN = Sqrt[(u - 15/16)^2 - 2/5 (u + 17/16) + 1/25] (I10 (u^2) - 1/u);
PA = Integrate[FXN /. {I10 -> 1/2 Log[1/2]}, u];
PB = Integrate[FXN, u] /...
Homework Statement
A flat ring of inner radius R1 and outer radius R2 carries a uniform surface charge density σ. Determine the electric potential at points along the axis (the x axis). [Hint: Try substituting variables.]
Homework Equations
V = (kQ)/r
The Attempt at a Solution...
Here's the problem I was given:
Find the area of the surface generated by revolving the curve
x=\frac{e^y + e^{-y} }{2}
from 0 \leq y \leq ln(2) about the y-axis.
I tried the normal route first...
g(y) = x = \frac{1}{2} (e^y + e^{-y})
g'(y) = dx/dy = \frac{1}{2} (e^y - e^{-y})
S = \int...
Homework Statement
Find the area of the surface generated by revolving the curve
x=\frac{e^y + e^{-y} }{2}
from 0 \leq y \leq ln(2) about the y-axis.
The Attempt at a Solution
I tried the normal route first...
g(y) = x = \frac{1}{2} (e^y + e^{-y})
g'(y) = dx/dy = \frac{1}{2}...
Homework Statement
I am suppost to integrate e^x^2 from 0 to 1 and such, I using Maclaurins rule, I got e^x=1+x/1!+x^2/2!+...+x^n/n!+e^(öx)*x^n+1/(n+1)!, 0<ö<1.
But when I put in x^2 instead of x, I end up with a legit thing except e^(öx^2)x^n+1/(n+1)! and this is giving me e^x^2 again!
I'm wondering how to integrate something of the form 2^x * e^x.
I tried using integration by parts, ∫u dv = v*u - ∫v du. The problem is no matter which term I choose to integrate and which to differentiate, the final solution still has an integral with a product of terms in the form (2^x)...
Homework Statement
This function of one variable need to be integrated: f(x)=1/(9+7*(sinx)^2) from x=0 to x=pi, without help with calculators or computer algebra software. Homework Equations
Have no idea.
The Attempt at a Solution
Have no idea.
I don't have any idea how to start. Please...
Homework Statement
Integrate sqrt(1+4x^2)
limits x = 0 to x = 1
Homework Equations
The Attempt at a Solution
let 2x = sinhu
I = 0.5 ∫ (coshu)^2du
limits u = 0 u = sinh^-1(2)
0.5 ∫ (e^2u +e^-2u +2)/4 du
0.5 [(e^2u)/8 -(e^-2u)/8 +2u]
I = 2.56 which is wrong :(
why is it wrong?
please help!
Homework Statement
I have to find the ratio of RB/RA where R is electrical resistance.
Both objects A and B have circular cross section and length L, and are made of the same material.
A has radius r0. B has radius r0/2 at the bottom and increases linearly to 2r0.
Homework Equations...