Integration Definition and 1000 Threads

Homework Statement I'm working on a generalization of gravitation to n dimensions. I'm trying to compute gravitational attraction experienced by a point mass y due to a uniform mass distribution throughout a ball of radius a -- B(0, a). Homework Equations 3. The Attempt at a Solution [/B]...

Hello, I am writing a program on Fortran to calculate the integral of sin^4(x) between x = 0 and x = π/2. I believe I know how to write the correct code, but I am unsure what the if statement should be for whether or not a point is inside the desired area. Any thoughts? Thanks.

1. The problem statement, all given data I've been working through one of the lessons for my HNC and I'm totally stuck on how they got from 27.84x10^-6 to 3.593x10^4. I can follow it all fine including the integration after that section it's just the inbetween that I can't seem to get my head...

Homework Statement Derive that: Correction (from a later post) The integral on the left side should be ##\int \cos^m(x)\sin^n(x)~dx## Homework Equations - The Attempt at a Solution Anyone can help me on how to start? ## u = cos^m x ## ## du = m cos^{m-1} x ## ## dv = sin^n x dx ## ## v...

Homework Statement Find the volume of the solid enclosed by the paraboloid z=x^2 + 3y^2 and the planes x=0, y=x, y=1, z=0 Homework Equations I'm not really sure what's getting me about this, but I'm not really sure how to proceed after finding the x, y, and z intercepts... The Attempt at a...

Homework Statement ## \int {sin} \frac{\pi x} {L} dx ##Homework Equations u substitution The Attempt at a Solution If i make ## u = \frac{\pi x} {L} ## and then derive u I get ## \frac {\pi}{L} ## yet the final solution has ## \frac {L}{\pi} ## The final solution is ## \frac {L}{\pi} - cos...

Hi, I've got this problem that I've been trying to work out. I think most of my problems come from the fact that I am not yet well versed in u substitution when it comes to integrals. I'm also not 100% sure what the problem is asking. I've tried doing a couple of things, but they don't seem to...

1. The graphs intersect where the functions are equal, so $\displaystyle \begin{align*} 6 - x^2 &= 3 - 2\,x \\ 0 &= x^2 - 2\,x - 3 \\ 0 &= \left( x - 3 \right) \left( x + 1 \right) \\ x &= 3 \textrm{ or } x = -1 \end{align*}$ The higher function is $\displaystyle \begin{align*} y = 6 - x^2...

x = 2y - y2 x = y

$\textsf{Reverse the order of integration in the following integral }$ \begin{align*}\displaystyle I&=\int_0^1 \int_2^{2e^x}f(x,y) \quad dy \, dx \end{align*} $\textit{From the integral we have that}$ $$0\leq x\leq 1 \quad \textit{and} \quad 2\leq y\leq 2e^x$$ $\textit{So, we get that}$...

Homework Statement :[/B] I was learning the use of standard forms in method of substitution in solving integration. My book has given this method for solving integrals of the type ##\int \frac{lx +m}{ax^2+bx+c} dx##: As an example, the book gives this one: Homework Equations :[/B] The...

Homework Statement Attached is a picture.. the book went from (-1 + \frac {2}{1+u} ) du + \frac {dx}{x} = 0 Edited by moderator. to -u + 2ln(1+u) + ln(x) = ln(c) Homework EquationsThe Attempt at a Solution How in the world could the integral of 0 be ln(c)? Maybe because it's 5 am and...

Hi guys. I’m looking at the brute force way at getting the E-field for a uniformly spherical charge distribution. The location of the E-field of interest is anywhere outside of the sphere. Here are some images Everything makes sense. I’m just not sure why the bounds for ‘s’ where z-r to...

Homework Statement What is the integral of e(x)2 over (x-1)2Homework Equations integral of (x-1)-2 is -(x-1)-1 and derivative of e(x)2 is 2xe(x)2 The Attempt at a Solution I tried to integrate it by part but I couldn't get a solution. I want to know how to start solving this question.

I am reviewing Calculus 1 integration learned long ago in the 1990s. Integrate (1/x) dx from 1 to 4. The textbook answer is ln 4. However, many of my friends tell me that the answer can also be written as log 4. But, ln 4 does NOT equal log 4. In fact, ln 4 > log 4. Who is right? Why?

- check if right check if right Now, 2 seems to be the right answer for A yet when i made x=5 and subtracted new form form the old one I got a difference of ~$\frac{4}{9}$ (should be 0 obviously) I got A=2 B=$\frac{45}{21}$ C=2 How to calculate $\lim_{{x}\to{\infty}}(- e^{-x})$

Homework Statement I have a function showing the volume of water in a bay at different times in the day, and I want to know what the area under this curve would represent (if it represents anything meaningful). I know how to integrate, so that isn't a problem. Homework Equations I am...

Homework Statement Let E be the ellipsoid x^2 + 2xy +5y^ +4z^2 = 1 Find the Volume of E Homework Equations None, just various integration methods. The Attempt at a Solution I know we're not supposed to say 'I don't know where to start' but with this one I really don't. If the best approach...

The curve has a gradient function dy/dx = 2 +q/(5x^2) where q is a constant, and a turning point at (0.5, -4). Find the value of q. option 1 : 2.5 option 2: -2.5 option 3: 0 Option 4: -3 I couldn't find the answer and will need assistance to how the answer can be obtained. I have...

Homework Statement I want to change the integration limits of an integral in cylindrical to cartesian coordinates. For example the integral of function f(r) evaluated between b and R: ∫ f(r)dr for r=b and r=R (there is no angular dependence). For write de function in cartesian coordinates...

I have defined a series of functions below with the end function `fA` being inserted for a numerical integration. The integration is with respect with one variable so the other arguments are passed as numeric so that the integration method (quad) may proceed import numpy import...

1. The problem statement, a ll variables and given/known data Homework Equations The Attempt at a Solution what is t equal to here , how should i think it ?

Homework Statement Could someone illustrate why $$\int_{V} \nabla \cdot (f\vec{A}) \ dv = \int_{V} f( \nabla \cdot \vec{A} ) \ dv + \int_{V} \vec{A} \cdot (\nabla f ) \ dv = \oint f\vec{A} \cdot \ d\vec{a}$$ ? Homework EquationsThe Attempt at a Solution I understand that the integrand can...

Homework Statement A ##10 cm## (on y axis) by ##10 cm## (on z axis) flat plate is located ##5 cm## away (on x axis) from a point charge ##q##. Calculate the electric flux from the point charge to the plate. Can somebody solve it using surface integral using both spherical and cartesian...

Homework Statement if ## f(x)= \int_x^3 \sqrt {1+t^{16}} dt ## find f'(x)Homework EquationsThe Attempt at a Solution let ## x = 1+t^{16},## → ##\frac {dx}{dt},= 16t^{15},## ## y= x^{1/2} ## →##\frac {dy} {dx},= 0.5x^{-0.5}##

Hi PF! Suppose I have two functions ##f(x),\,g(y)## that are numerically defined as vectors (i.e. ##g(y) = [0,1,4,9,16]:y = [0,1,2,3,4]## and say ##f(x) = [0,1,8,27,64]:x = [0,1,2,3,4]##) and am trying to compute $$\int_0^1 f(x) \int_x^1 g(y)\, dydx.$$ How would I do this in MATLAB? I could be...

Hello everyone! I'm having a bit of a problem with comprehension of the Cauchy integration formula. I might be missing some key know-how, so I'm asking for any sort of help and/or guideline on how to tackle similar problems. I thank anyone willing to take a look at my post! Homework Statement...

Homework Statement Homework Equations I've drawn graph below. The Attempt at a Solution Currently their limits are y = 0 to y = x - 2 vertical arrow and x = 2 to x = infinite. horizontal arrow Changing limits i get right side graph. x = y + 2 to x = infinite horizontal arrow y = 0 to y =...

Homework Statement For R > 0, assume ΓR is a circle {z ∈ C : |z| = R} with anticlockwise direction. For which R>0, does the the function f(z) = 1/sin^(2)(z) be continuous on ΓR and evaluate ∫_{ΓR} dz/sin^(2)(z) for each R (the answer may be dependent on R). Homework Equations sinx= (e^(ix)...

Homework Statement integration with respect to x Homework Equations integral 1/sqrt (a^2 - x^2) = arcsin(x/a) The Attempt at a Solution image attached, the arcsine term in 5/2 arcsin((2x-5)/5) it should be 5 arcsine(sqrt(x/5))

Homework Statement This is just the triple integral of an easy matrix problem. I just have no ideas what they got by the time they got to the integral of x. Homework Equations integral[/B]The Attempt at a Solution Somebody please prove me wrong. I got a matrix of constants by the time I got...

If you are trying to find the integral of a function with a complex pole on the real axis (i.e. ##[-\infty,\infty]##) via analytic continuation, does it matter if you integrate along a contour either in the upper-half plane or lower-half plane? I was under the assumption that either approach was...

Hi, I've been following a derivation of relativistic kinetic energy. I've seen other ways to get the end result but I'm interested in finding out where I've gone wrong here: I'm struggling with integrating by parts. The author goes from...

Homework Statement How do I solve ##\frac{20\ln{(t)}}{t}##? Homework EquationsThe Attempt at a Solution Is it easier to calculate this without integrating by parts? I'm not sure where to start.

Homework Statement Trying to help a friend with a problem. We are supposed to solve the below using polar coordinates. The actual answer is supposed to be π/16. Solving the integral is not the issue, just converting it. 2. The attempt at a solution What I got sort of worked, but it is only...

Homework Statement in the textbook, it says: how does the integral of y'' gives you y' like that? Homework Equations given C_a is a dimensionless peak acceleration factor. The Attempt at a Solution [/B]

Hello, I know that the derivative of Dirac-delta function (##\delta'(x-x') = \frac{d}{dx} (\delta(x-x')))## does the following: ##\int_{-\infty}^{\infty}\psi(x')*\delta'(x-x') dx' = \frac{d\psi(x)}{dx}## it is easy to visualize how the delta function and the function ##\psi(x')## interact along...

Homework Statement A particle that can move along the x-axis experiences an interaction force Fx=(3x2−5x) N where x is in m. Find an expression for the system's potential energy. Express your answer in terms of the variables x and the constant of integration C, where C is in joules. Homework...

Homework Statement Hi I was wondering if anyone could give me a hand with this problem I'm trying to solve. I am trying to integrate this equation twice. I'm not really sure what to do with the right hand side of the equation.Homework Equations The Attempt at a Solution [/B] The left side...

Homework Statement Calculate the geometric phase change when the infinite square well expands adiabatically from width w1 to w2.Homework Equations Geometric phase: \gamma_n(t) = i \int_{R_i}^{R_f} \Bigg< \psi_n \Bigg | \frac{\partial \psi_n}{\partial R} \Bigg > dR Infinite square well wave...

Homework Statement I wish to find the area under the curve y = 1/2^x between x=0 and x=1 but get an answer that is half the expected answer.Homework Equations Integrate y = 1/2^x to get -1/(2^x ln2) + Const This integration result was confirmed on Wolfram Slot in the range x = 0 to x = 1...

Hello everyone I have the following question regarding numerical integration twice from acceleration to displacement. Suppose that a particle has acceleration function of a = tt (which has non-elementary integral), to find the velocity it is easy as I can use Simpson's rule for numerical...

Homework Statement Integrate ∫ (tan √x) / (2 √x) dx Homework Equations Limits from 0 to ∞ The Attempt at a Solution Put u = √x du/dx = 1/ (2 √x) dx = du * (2 √x) now question becomes ∫ tan u du = log sec u = log (sec √x) now applying limits ∫ tan u du = log (sec √∞) - log (sec √0) = log...

Homework Statement I'm trying to change the bounds for this integral Sin(x^2)dxdy With x going from 1 to 2y, y going from 0 to 1 (I already know the integration for sin(x^2) The Attempt at a Solution I converted 2y=x to 1/2x=y and graphed all the bounds. I went with 1,2 for my...

Homework Statement Homework Equations in the pic The Attempt at a Solution why is there an extra "r" in the highlighted line? my attempt: ## \int_0^{2\pi}\int_0^2\int_{r^2}^41\ dy\ r\ dr\ d\theta ## = ##\int_0^{2\pi}\int_0^2\left(4-r^2\right)\ r\ dr\ d\theta## thanks

Homework Statement For an analytic function, f(x+iy)=u(x,y)+iv(x,y),u is given by u=(3x^2) -(3y^2). The expression for v, considering K to be a constant is? Homework Equations δu/δx=δv/δy δu/δy=-δv/δx [/B] The Attempt at a Solution My attempt :- u=(3x^2) -(3y^2) δu/δx=6x &...

Homework Statement Mathematica vs (Symbolab + my brain) Homework EquationsThe Attempt at a Solution I think this integral calculation in Mathematica is wrong. Open pictures below. Please help me. Graphs (the red one is under the blue and the green): https://ibb.co/bACa3G Wolfram Mathematica...

Homework Statement The differential equation of motion for the simple pendulum can be shown to be ##\ddot {θ} = -(g/L)sinθ##. Given that L=9.81 m and that the pendulum is released from rest at θ=60deg, determine the time required for the pendulum to reach the position θ=0deg. Use Δt=0.10s, and...

Homework Statement Homework Equations cos2x = (1+cos2x)/2 sin2x = (1-cos2x)/2 The Attempt at a Solution I believe you would use the double angle formula repeatedly but that is very tedious; is there a more concise way to solve the problem?

Dear Forumers,Given a simulink model: http://www.femm.info/Archives/contrib/images/TransientLoudspeaker/SimulinkOverview.png I would like to implement fast code for it.I have no access to matlib or simulink at all, so I tried to implement the simulation in C code. Code for the block...