Integrating Definition and 940 Threads

Homework Statement Revolve the region bounded by x=0, x=1, y=0 and y=x^5 about the y-axis use shells to find the volume I know how to set up the integral I just don't know where I'm integrating from. Is it from 0 to 1?

I couldn't figure out what to do with this type of integration \int (a x^{2}+ bx +c) ^{\frac{m}{n}}dx here m, n are integer numbers. Integration limit -∞ to +∞. Will Binomial expansion work? Please give me some clue.

Integrating exp(x^2) like gaussian integral?? Hi, I can't solve this integral \int^{1}_{0}\\e^{x^2}\\dx Can I solve this integral like gaussian integral? Please help me Thanks.

Homework Statement ∫ e^(\pix^2) dx, with limits -∞ to ∞ Homework Equations ∫∫ dxdy = ∫∫ rdrdθ The Attempt at a Solution Hi, here's what I've done so far: Introduce a dummy variable y to get ∫∫ e^\pi(x^2 + y^2) dxdy, with limits -∞ to ∞ for both dx and dy...

Homework Statement \int 59x(cos(x))2 dx Homework Equations The Attempt at a Solution I tried doing integration by parts with u= (cos(x))2 and dv= xdx v= \frac{x^2}{2} However this didnt get me very far can some one tell me what the first step or two are.

I am a little confused here. If the integral of f'(x)/f(x)= ln|f(x)| +k then say the below equations which are the same give different results? 2/(2x+2) The top is a derivative of the bottom, so the integral is ln|2x+2|+k 1(x+1) This is the same as the first equation. The top is also...

Hey I'm having problems trying to integrate my function func1 in MATLAB. Really don't know where I am going wrong so would really appreciate if anyone could help. The code I'm using is below, thanks: Function Mfile: function [ f1 ] = func1( E, Delta, kB, Temp ) %func1: calculates...

I'm supposed to be Integrating 1/(4+x^2)^2 dx using trigonometric substitutions, but I do not know how to get started with this one. Am I supposed to rewrite this as 1/sqrt((4+x^2)^2) and then use the reference triangle? I've tried expanding the bottom, but that doesn't get me anywhere...

Homework Statement Find a power series representation for the given function using termwise integration. f(x) = \int_{0}^{x} \frac{1-e^{-t^2}}{t^2} dt Homework Equations The Attempt at a Solution Well, I figured I could rewrite it like this using the Maclaurin series for...

Finding the integrating factor (ODEs) [Solved] Working on this problem, I can't figure out why we take the derivative of \mu with respect to y, and what to do when our integrating factor is a function of both x and y. In the case below, it ended up being separable, but what can you do if it's...

Hi, this isn't a homework question, I'm just curious about this. I am wondering what the correct notation is for the integral of F(x). For example, integral of f''(x) = f'(x) + c integral of f'(x) = f(x) + d integral of f(x) = F(x) + e integral of F(x) = ?? I feel silly for not...

Homework Statement Calculate \int _{\mathbb{R}^{3+}} V(\textbf{r} ) d\textbf{r} where V(\textbf{r})=\frac{1}{r},\ \ r=||\textbf{r}|| The Attempt at a Solution I'm guessing \textbf{r}=x \textbf{i} + y \textbf{j} + z \textbf{k} so r=\sqrt{x^2+y^2+z^2} and d\textbf{r}=...

Hi guys, this is my first post but have read the forums for a long time - a quick search didnt bring up anything that could help me. So i was wondering if someone could please explain something to me. I have a differential equation (excuse the pictures, I don't know how to use the equation...

For the first question, I am only supposed to find the general solution of the differential equation. 1) dy/dt = -2ty + 4e^(-t^2) dy/dt + 2ty = 4e^(-t^2) Integrating factor = e^(Integral of 2t) = e^(t^2) Multiply both sides by IF: e^(t^2) * (dy/dt +2ty) = 4e^(t^2-t) e^(t^2)*dy/dt...

Homework Statement Solving this differential equation ty' + 2y = t^2 - t + 1 Homework Equations Its linear so i set it up in linear form y' + y(2/t) = t - 1 +1/t The Attempt at a Solution the integrating factor (u) = e ^ integral (ydt) = e^ integral (2dt/t)... Here's the...

Hello :smile: I've been stuck on this question for almost 3 hours now, and I still have no idea what to do. We haven't done a question like this in class, although we have done integration with partial fractions. Homework Statement Evaluate...

Homework Statement provided with data that dq = rho(r) *4phi*r^2*dr rho(r) = [Q*e^(-r/R) / 4phi R *r^2) I have to show that the charge q(r) enclosed in a sphere of radius r is q(r) = Q(1-e^(-r/R)) by using appropriate integral. how the integral should be? Homework Equations The...

Homework Statement Find the integral of (1-x)((2x-x^2)^.5) dx Homework Equations The Attempt at a Solution I am kind of hazy on U substitutions but I thought that was the right way to go here: let u=2x-x^2 du=2-2x (1/2) Integral of (u)^.5 du < i wasn't sure if I went wrong...

Homework Statement The ODE is (1+x)*dy/dx - xy = x+x^2 Homework Equations The method of solution is to be through the use of the integration factor. The Attempt at a Solution First, I divided each side by (1+x) to produce dy/dx - xy/(1+x) = x then factor out the x on...

Homework Statement I need to integrate (2x-5)/(x^2+5x+11) Homework Equations The Attempt at a Solution My problem is just finding a formula for an irreducable quadratic. I know if the denominator was x(x^2+1), I would use A/x+(Bx+C)/(x^2+1). I just don't know the formula in this...

During one lecture it was mentioned that equations of the form P(x,y)dx+Q(x,y)dy=0 always have at least one integrating factor. But the lecturer didn't know the proof, I've tried using Google but no luck. Anybody can show me the proof? Thanks a lot.

I'm using a 3rd party physics engine to run rigid body physics. It just updates the bodies once every 16 ms or so. I'm trying to write an algorithm to predict where free-falling bodies will be in 2 seconds using standard physics equations. I'm having trouble with predicting angular velocity and...

Hi guys, Does anyone have any ideas about an analytical solution for the following integral? \int_{0}^{2\pi}J_{m}\left(z_{1}\cos\theta\right)J_{n}\left(z_{2}\sin\theta\right)d\theta J_{m}\left(\right) is a Bessel function of the first kind of order m. Thanks.

The question is If f(x) = 7x^3 + 8x^2 - x + 11, evaluate : a, Integral +1 - -1 f(x) dx b, Integral +1 - -1 f'(x) dx c, Integral +1 - -1 f''(x) dx For a, Just integrate each individual and then input the figures which gave me 1.75x^4 + (8x^3)/3 - 0.5x^2 + 11x Which when I input...

Homework Statement As I was reviewing some of my previuosly learned calculus I came across somthing that I had either forgoten how to do or was never taught. How do you take the integral of somthing like this \int \sqrt{\frac{9}{4}x+1} I don't know how to start with this one. Do I use U...

Hi Guys, Ive gone through a 3 year physics degree but can't remember ever touching on this? I am doing some work and some of the theory contains integrals of d2x or d3R for instance. I have no idea how to do these. Any help? Thanks all

Hi every body I am trying to intergrate the following function using Maple: j2out(x):=c2*x*exp(int((s-vout(s))/s/vout(s),s=0.0015..x)); where vout(s)=0.07595560773650. C2 is constant but when I do, it returns a symbolic answers i.e Maple just returns the original expression without...

Homework Statement Find \int\int\int y^2 z^2where E is the region bounded by the paraboloid x = 1 - y22 - z2 and the plane x = 0. The Attempt at a Solution The region is a paraboloid with vertex at x = 1, y = 0, z = 0. I chose z bounds to be between 0 and 1 - y22 - z2 for first integral...

I need some explanation regarding a solution found in our textbook. The example starts with this DE: (1) y(x3 - y)dx - x(x3 + y)dy = 0. By regrouping, exact DEs will be found and the equation can be rewritten to: (2) x3 d(\frac{x}{y}) - \frac{d(xy)}{y} = 0. The integrating factor is found...

Homework Statement Integrate: \frac{Log[1+x]}{1+x^{2}} Homework Equations Integration by parts. The Attempt at a Solution If the integration is easier than what I think. Please let me know how to get started. I used integration by parts to get uptil here...

Homework Statement \int\sqrt{2*x-1} Homework Equations The Attempt at a Solution Homework Statement Obviously this can be fixed with the antiderivative of a linear function with proper constants i.e. \int A\times f(bx + c) = \frac{A}{b} F(bx + c), however my instructor provided...

I was thinking about how to approximate pi accurately and came up with something and all the calculations i did seem to show that its true and I am wondering if its used often for calculating pi or if there is something better? radius of this circle equals 1 and therefore calcualting a...

Homework Statement give the general solution of the following equation x' = tx + 6te-t2 Homework Equations for x'+p(t)x=q(t) xeI=\intq(t)eIdt where I=\intp(t)dt integration by parts \intf'g = [fg] - \intfg' The Attempt at a Solution x'-tx=6te-2t I=\int-t dt = -t2/2...

Homework Statement Integrate the square root of (x^2 -1) over the interval 0-1. The attempt at a solution First off, I know this is a quarter of a circle, but I'm not supposed to solve it that way. Now then: x = sec theta dx= sec tan theta. square root (x^2-1) dx becomes...

Homework Statement \int{\frac{xsec^2x}{tanx+\sqrt{3}}}dx The Attempt at a Solution I let tanx+\sqrt{3}=u Then, \frac{du}{dx}=sec^2x , dx=\frac{du}{sec^2x} Substituting into the integral: \int{\frac{x}{u}du But now I don't know what to do. That little x is really screwing me...

Im doing a bit of contour integration, and a question came up with a term in it am unsure of how to do: in its simplest form it would be \int\bar{z}dz where z is a complex number and \bar{z} is it's conjugate. Hmm i can't get the formatting to work out properly.. :S

Homework Statement By using the substitution u=cosx obtain the value of the integral \int\delta(cosx-1/2)dx between 0 and pi Homework Equations I have no idea how to go any further with this apart from substituting in for u!? The Attempt at a Solution

I am reading a thermodynamics book. I am confused on how they say use the chain rule Here. it makes no sense to me how they go from dV/dt to (dV/ds)(ds/dt) . I know how the chain rule works ,just don't know where they got these values

Homework Statement grad f = (3x2 + y2)i + (2xy - 3)j a) find f b) evalue the integral of grad f dot dr where c is any path from 1,2 to 2,1 c)evaluate the integral of gradf dot dr where c is the curve given by 4x2 + 9y2 = 36 Homework Equations The Attempt at a Solution...

What are some techniques for integrating functions that are or contain radicals? I am familiar with trigonometric substitution. Are there any other "common" techniques or special functions that can be used to integrate these functions? or does trigonometric substitution basically take care of...

I'm supposed to integrate w/w^4 + 1 The two ideas I'd come up with was trying to substitute w^4+1 with u but that results in a 0 in the numerator. Then I thought maybe I have to put w/w^4+1 into the 1/1+w^2 form and integrate into 1/k tan^-1kx + C but I'm not sure how to keep the original...

Homework Statement 1.) \int{\frac{t}{(1+t^{2})^3}dt} 2.) \int{xe^{-2x}dx.} 3.) \int{\frac{x.dx}{2+x^{2}}} This one is inegrating between 2 and 0, but I didn't know how to format that in. 4.) \int{\frac{cos t}{1 + sin t}dt.} Homework Equations Q 1.) I'm substituting u =...

Homework Statement Hi all. My question has to do with integrating rational functions over the unit circle. My example is taken from here (page 2-3): http://www.maths.mq.edu.au/%7Ewchen/lnicafolder/ica11.pdf We wish to integrate the following \int_0^{2\pi } {\frac{{d\theta }}{{a + \cos...

Homework Statement say I have \vec{F} = ye^x\vec{i} + e^x\vec{j} and C the line segment from the point (1,4,-2) to the point (6,7,-2).I need to find: \int\limits_C \vec{F} d\vec{r} Homework Equations The Attempt at a Solution First I parametrize C as: \vec{r} = 6 + 5t \vec{i} + 7+3t...

is there an exact way to calculate the volume of a shape where one shape is revolved around a parabolic curve (obviously with limits). i don't know much about this stuff but I am pretty sure u need to integrate it. the shape revolved is a rectangle (vertical) with a triangle connected at the...

(x^2).e^(-2a(x^2)) how would i integrate this? By parts? If so using |udv = uv - |vdu (hope that's right) would i let u = x^2 and dv = e^(-2a(x^2)) ? but how do I integrate dv = e^(-2a(x^2)) to find v ? any help appreciated :)

Homework Statement Integral (pi1/2, 0) of Integral (pi1/2, y) sin(y2) dxdy Homework Equations This one is interesting because it can't be integrated as is (at least not at the level of my course) but I think with some rearranging it can be done. I was wondering if anyone could verify...

what next ? TNX !

Homework Statement y' = 2xy/(x^2-y^2) answer: Cy = x^2 + y^2 Homework Equations The Attempt at a Solution dy/dx = 2xy/(x^2-y^2) dy = [2xy/(x^2-y^2)]dx how do i separate the variables?

Hi, I am trying to solve the following problem (but note you can skip the details and look at the last equation and help me with the integral): a small planet (mass m) is found at rest relative to the Sun (mass M) with a separation distance x_{0}. Consider now the small planet move in response...