Integrating Definition and 940 Threads

$\int x (5^{-x^2})dx= -\frac{1}{2} \int 5^{-x^{2}}(-2x)dx$ how is $\frac{1}{2}$ in front of the $\int$ derived

\begin{alignat*}{3} u_t(r,\theta,0) & = & \delta(\mathbf{x} - \mathbf{x}_0) & = & \delta(r - r_0, \theta - \theta_0) \end{alignat*} $$ \int_A\delta(\mathbf{x} - \mathbf{x}_0)f(r,\theta)dA = \int_0^{2\pi}\int_0^a\delta(r - r_0, \theta - \theta_0)f(r,\theta)rdrd\theta = f(\mathbf{x}_0) $$ How do...

$$ \int (\ln x)^pdx, \quad p > 0 $$ How do I go about integrating this?

Check this out: \int_{-1}^{0} ln(x) dx u=ln(x), dv=dx du=\frac{1}{x},v=x \int_{-1}^{0} ln(x) dx= x\space ln(x) \|_{-1}^{0} -\int_{-1}^{0} \frac{x}{x} dx =x\space ln(x) \|_{-1}^{0}-x \|_{-1}^{0} =\lim_{x\to0} x\space ln(x)-(-ln(-1))-(0-(-1)) \lim_{x\to0} x\space ln(x)=lim_{x\to0}...

When I integrate v(t) after I calculated the t, what do I get? Let;s say t=2. do I get the position vector in this 2s? If so it means the integral goes from 0 to t? or I still need to calculate from 2 to t? I could simply integrate v from 0 to t then place 2 in the position vector but I got an...

Hi, I am doing self study and have hit a snag in the road. Can someone please clarfiy this for me. I am reading K.A. Stroud's Engineering Mathematics which so far has been great.Consider the equation \frac{dy}{dx} + 5y = e2x In this case, we begin multiplying both sides by e5x. This gives...

Hi, I am doing self study and have hit a snag in the road. Can someone please clarfiy this for me. I am reading K.A. Stroud's Engineering Mathematics which so far has been great. Consider the equation \frac{dy}{dx} + 5y = e2x In this case, we begin multiplying both sides by e5x. This...

Integrating the delta function: $$ \frac{4}{\pi^2}\int_0^{\pi}\int_0^{\pi}\delta(x - x_0,y - y_0)\sin nx\sin my dxdy $$ Would the solution be $\frac{4}{\pi^2}\sin nx_0\sin my_0$?

Homework Statement if v = 8t - 3t^2 and the body is at P find where the body is from P when t=3 The Attempt at a Solution I am very new to calculus and have just been taught basics of differentiation and integration. I know that when you integrate there is an arbitrary constant so I have...

I have this code that i have been working on that will interpolate and integrate some data. I need to read this data from a file with unknown rows and columns to a two dimensional array/matrix so that the data can be broken down further into one dimensional arrays from the parent 2D array's...

Let the Wronskian between the functions f and g to be 3e^{4t}, if f(t) = e^{2t}, then what is g(t)? So the Wronskian setup is pretty easy W(t) = fg' - f'g = 3e^{4t} f = e^{2t} f' = 2e^{2t} So plugging it in I would get: e^{2t}g' - 2e^{2t}g = 3e^{4t} Which results in g' - 2g...

Whenever I'm given a SDE problem that requires us to multiply both sides by an "integrating-factor", it's always given to us as a *Hint*. I would like to know how to come up with these integrating factors. Here's some examples: 1) For the mean-reverting Ornstein-Uhlenbeck (OU) SDE dX_t =...

Hi, I am trying to integrate (tanh(x)+coth(x))/((cosh(x))^2) I am substituting u=tanh(x), du=dx/((cosh(x))^2) and end up with 1/2(tanh(x))^2 + ln |tanh(x)| + C which is incorrect. What am I doing wrong??

Homework Statement Find <x> in terms of X0 if X0 is constant and \Psi(x) = \frac{1}{\sqrt{X_0}}e^{\frac{-|x|}{X_0}} and <x> = \int^{\infty}_{-\infty}{\Psi^* x \Psi}dx where Psi* is the complex conjugate of Psi. Since there is no imaginary component, this is effectively Psi2. so, from...

Homework Statement How to integrate ∫1/(1+√tanx) dx? 2. The attempt at a solution Tried to substitute √tanx with z, but ultimately getting messed up with large expression

Hi all. I am having Calculus 1 this year. We are using a book called Thomas Calculus. I think its a lot of fun, but I have to work very much since there is basic stuff like trigonometry that I know really bad. Since I work so much with math I thought it could be fun and helpful to talk with...

Homework Statement Find $$\int_{C} \frac{ds}{(2y^2+1)^{3/2}}$$ where $$C$$ is the parabola $$ z^2=x^2+y^2 , x+z=1$$ Homework Equations The Attempt at a Solution I tried to parametrize the C , s.t$$ x=t, z=1-t, y=\sqrt{2t-1}$$ , but it seems to become a mess, and I don't know the...

Homework Statement Find an integrating factor for the first order linear differential equation \frac{dy}{dx} - \frac{y}{x} = xe^{2x} and hence find its general solution Homework Equations The Attempt at a Solution I found the integrating factor which is e^{-lnx} = x^{-1} and...

Homework Statement Homework Equations The above formulas The Attempt at a Solution I'm lost on where to start with this. The object has an intial velocity in the X direction and has the resistive force of the plontons acting upon it when it lands. What exactly is the equation...

My question is: If you have a E= Ex+Ey+Ez To find V(x,y,z), i should: Just integrate Ex in order x? ∂V(x,y,z)/∂x = -Ex so: -V(x,y,z) = ∫Exdx or have i to sum the three integrals? -V(x,y,z) = ∫Exdx + ∫Eydy +∫Ezdz

I'm sure this is an easy question to answer - per the attached image, can someone please explain why the friction force has not required/been affected by integration? My calculus is very rusty but the only reason I can think of is that μ, m and g are all constants (for the purposes of the...

Homework Statement I need some help understanding an integral step in the example below. I get how the integrand was set up, but I don't get how comes to two expressions with the absolute value of z-L/2. (Problem description if that is needed: L is the length of a cylinder with radius R, and P...

When looking at example 3 in this pdf: http://www.physics.isu.edu/~hackmart/centerofmass.pdf where it shows how to find the Center of Mass of a Nonuniform Rod. I was wondering when or what you have to know in order to integrate over dm rather than changing the variables in terms of dx.

Homework Statement I'm having a hard time to solve the following DE using an integrating factor, I'm asked to find one and solve the DE. (x+y^2)-2xyy'=0.Homework Equations The Attempt at a Solution If I call u=u(x) (I assume the integrating factor depends only on x, not on y), the following...

Suppose one needs to evaluate a definite integral over a singularity, like: -\int_{-1}^3 \frac{1}{x^2} dx The textbook way to do so is to split the integral into two parts around the singularity and take the limit, like so: \lim_{b\rightarrow 0} -\int_{-1}^b \frac{1}{x^2} dx and...

I am asked a problem where I'm supposed to integrate the expectation value of a dynamic variable (operator) to solve a differential equation. OK, is the expectation value supposed to be a variable? But it seems to me like its a definite integral over allspace and thus is a number. So...

∫(cot^4 x) (csc^4 x) dx Wolfram wants to use the reduction formula, but I'm meant to do this just using identities and u substitution. I was thinking something along the lines of: =∫cot^4 x (cot^2 x + 1)^2 dx =∫cot^8 x + 2cot^6 x + cot^4 x dx but I don't know where to go from there.

Homework Statement From Elementary Differential Equation by Boyce and Diprima Chapter 2 Miscellaneous Problems #11 (x^2+y)dx + (x+e^x)dy = 0 ANS:(x^3/3)+xy+e^x=c Homework Equations multiplying an integrating factor to make the DE exact: 1. du/dx = u(My - Nx)/ N 2. du/dx = u(Nx-My)/ M The...

Homework Statement Please help me understand the reason for substituting various trig identities into trig functions with powers instead of integration by parts. Does integration by parts not work on trig functions with powers, or is it just so much work that substituting trig identities to...

http://www.hardwaresecrets.com/imageview.php?image=3740 Referencing the above image, I have a few a questions. 1) I think CLK means clock input; does CLR perhaps mean clear? 2) What exactly is the role of the output buffer? 3) I'm confused as to how the control logic exactly functions and...

Hi i was wondering if i could get help with a question. A cone has a radius of 0.75m and a height of 4m. The density changes throughout the cone and can be modeled by the function ρ=3h^2+4h (h for height). Find the mass of the cone. Please help

I don't know how to apply Leibniz's rule for this integrand. I believe there is a substitution to allow me to express this integral differently, but the partial being a function of what we're integrating by is confusing me. \int^{b}_{a} \frac{\partial f(x,y)}{\partial y(x)} dx Knowns are that...

Okay this seems like it should be simple but I'm stuck. A particle moves from point A to point B in one dimension. The velocity of the particle changes with position according to some formula V = V(x). How long does it take for the particle to get from point A to point B? If I could write...

Homework Statement I=∫cot(x)dx Homework Equations wht's wrong in this approach (integrating by parts) The Attempt at a Solution...

Homework Statement Find the electric charge centred in a sphere of radius a, centered at the origin where the electric potential is found to be (in spherical coordinates) V(r)=kr^-2 where k is some constant. The Attempt at a Solution We have E=-\nabla V = -2kr^{-3} \hat{r} So...

We are in the process of talking with www.desmos.com about how we can integrate their graphing software on MHB in an easy-to-use way, similar to the Wolfram Widgets (hopefully). In the meantime I recommend their website for graphing 2-d equations. It's very easy to use and in my opinion is...

Hi! I hope this is the right forum... I am having trouble with Mathematica: Maybe someone could help out of his experience ? I created w[x]:=RandomReal[NormalDistribution[0,1],x] I got it's plot. Now I want to integrate it: I wish to receive another graph, which is the plot of the...

Homework Statement ∫√(1+x2)/x dx Homework Equations The Attempt at a Solution Let u = 1+x2 du = 2xdx 1/2du=xdx x=√(u-1) ∫√1+x2/x dx =∫√u/√(u-1) du or is it 1/2∫√udu as xdx would remove it. This is where I got confused.

I just want to clarify this. I have had trouble before with including the function in the integral when I am trying to find volume. I have come to think that this is necessarily only when it is a double integral. But I had a specific question I posted earlier and I feel like somebody told me...

I have a maths B assignment where I need to find the volume of a tunnel. We have been given two equations to describe the area of this tunnel. The teacher says that we haven't learned how to integrate at this level, and he has also said that the chain rule and product rule do not work for...

Homework Statement Hi An integration question: t= 1/(1+r2) Can you please show me how to integrate with respect to r. Thank you. The Attempt at a Solution ∴t = (1+r2)-1 I then tried substituting u = 1+r^2 but that didn't work! Is there a trick with this?

Hii Everyone, \int\frac{1}{x^{r}-1}dx where r is a real no. greater than 1regards, Bincy

I would like to integrate by parts this term- \mu^2 (\nabla^2)^{-1} (\nabla\times B)\dot{B} Here B is a vector and \dot{B} is the time derivative of B. And \mu is just a constant. Can anyone help me?

1. ∫\frac{dx}{x3 + 2x} We're suppose to evaluate the integral. Use Partial Fraction Decomposition: \frac{1}{x3 + 2x} = \frac{A}{x} + \frac{Bx + C}{x2 + 2} 1 = A(x2 + 2) + (Bx + C)(x) 1 = Ax2 + 2A + Bx2 + Cx 1 = x2( A + B) + Cx + 2A Solving for A gives \frac{1}{2} Solving for B...

Homework Statement I'm reading a chapter out of Elem. DE 6th Edition by Rainville and Bedient (Ch 4 pg 61) titled integrating factors found by inspection. To explain it, the authors start with an equation, which is grouped to become: y dx + x dy + x^3y^2 dy = 0 which then becomes...

Function is (x - 2xy + e^y) dx + (y - x^2 + xe^y) dy = 0 Okay so it is the standard convenient exact equation for newbies. Now here is the part that confuses me. (a) Let P(x,y) = (x - 2xy + e^y) dx & Q(x,y) = (y - x^2 + xe^y) dy The function is defined for all real Numbers on an x,y plane...

This is a problem that came to me when i was doing implicit differentiation and i got curious as to how to integrate a problem like this. I was fascinated by the simplicity if an equation would have a complex integration problem. Homework Statement ∫x^x(ln x + 1)dx, Question 1 ∫x^x dx...

Can someone tell me what the benefit of this is, and why it's been traditionally very hard? I've heard that many RF applications now do an S-i-P integration of an inductor, possibly for spatial and cost reasons.. What would be some considerations, though (i.e. does the inductor add any noise...

In an exercise with included solution I can't understand how integrating sin^2(ωt) gives T(period)/2 \intsin^2(ωt)dt = Period/2 I posted the whole problem below, because I had more doubts, but understood them typing up the problem. I appreciate any help. [SIZE="2"]YOU CAN...

I looked online and it gave a really simple method to solve it and it ended up with the solution x-2tan(x) I took a really weird approach and I'm not sure if my answer is right, and I'm hoping if someone could take the same approach and confirm if I did it correctly. I basically separated the...