Integrating Definition and 971 Threads

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...

I can see why y2 is an integrating factor, but I don't know how this answer can be derived. Do you use: \frac{N_{x}(x,y) - M_{y}(x,y)}{M(x,y)} Where M (x,y) = 4(x3/y2)+(3/y)]dx, and N = 3(x/y2)+4y dy When I try and solve this, I get a very complex integrating factor...

So I need to inegrate over a solid angle, in which every possible orientation is considered (we are doing scattering events in which we assume every possible angle is possible), thus I need to solve \int d\Omega_1 d\Omega_2 d\Omega_3 Eqn (1). Now I know \int^{2 \pi}_{0}...

Homework Statement In this problem, I am asked to find the total torque acting on a device consisting of two open half-cylinders connected to a shaft rotating in a fluid. To clarify, they are half-cylinders in the sense that they have been cut in half in the lengthwise direction and are...

Homework Statement The solid bounded by the parabolids z = 3x^2 + 3y^2 -7 and z = -x^2 -y^2 + 9 Homework Equations The Attempt at a Solution Ok so i set the two z equations into polar form and came up with 3r^2 = 7 and r^2 = 9 I thought that r went from (7/3) ^(1/2) to 3 and...

In the following problem how does -g end up becoming -g(m/g)? Isn't the derivative of -g just (-g^2/2)? http://users.on.net/~rohanlal/integfact.jpg

Okay well, I looked through my calculus notes and textbook and I can't find what to do when you are integrating a function of the type a/u where a is a constant and u is some linear function of x. I know that the integral of 1/x is ln(x) but what about when you have something like \int...

Homework Statement I want to compute \int_{C}^{}{|f(z)||dz|} along the contour C given by the curve y=x^2 using endpoints (0,0) and (1,1). I am to use f(z)=e^{i\cdot \texrm{arg}(z)} Homework Equations The Attempt at a Solution I know that for all complex numbers z, |e^{i\cdot...

Homework Statement integrate Homework Equations 1/(2x^2 + 3x + 1)[(3x^2 - 2x + 1)^(1/2)] The Attempt at a Solution

Homework Statement Indefinite integral: e^(4x+(e^4x)) Homework Equations I'm thinking integration by parts, involving UV minus integral of Vdu The Attempt at a Solution So I saw that this can be split into two: e^(4x) times e^(e^4x)). The latter is a bit complicated. I...

Homework Statement Please tell me how to integrate this... Homework Equations [(2x + 4)][(2x^2 + 3x + 1)^(1/2)] The Attempt at a Solution

Homework Statement The integral from 0 to pi/2 of 1/(1 + (tanx)^sqrt2) dx. Homework Equations trig identities? The Attempt at a Solution I tried some substitutions but it just made the problem more complicated. I also multiplied by (tanx)^sqrt2 in the numerator and denominator in...

Hey, I have been trying to make Mathematica integrate the following function: r_{e}=\frac{c}{H_{0}}\int_{0}^{z}\frac{dz}{\left[\Omega_{NR}(1+z)^{3}+\Omega_n(1+z)^{3-n}+\Omega_{\Lambda}\right]^{\frac{1}{2}}} There are two cases for which this equation needs to be integrated, seperately; (i)...

How do you integrate xsinxcosxdx

I'm trying to follow this example from class notes. x^2 \frac{{dy}}{{dx}} + xy = 1,\,\,y\left( 1 \right) = 2 Divide through by x^2 to set it up in a form for using the integrating factor method. \frac{{dy}}{{dx}} + \frac{y}{x} = - \frac{1}{{x^2 }} I'm not sure where the minus...

Hi! I want to know how to intergrat e^(-(x^2)/2) . Someone told me to use the intergration of e^x= 1+ x + (x^2) /2!+ ...(X^n)/n! ... is that sounds right?? and if it is i got pi as an answer for e^(-(x^2)/2) , is that the right answer?

Homework Statement The sequence fn: [-1,1] -> R, fn(x)= nxe-nx2 converges pointwise to f(x)= 0, x in [-1,1]. Can you verify the following: limn->\infty (\int^{1}_{0}fn(x)dx) = \int^{1}_{0} (limn->\infty fn(x))dx Homework Equations Theorem: If fn is continuous on the interval D for every...

Homework Statement I am having a problem integrating in a WKBJ semi-classic integral. Well it's this : I have to integrate \int_{0}^{\sqrt{m}E}\sqrt{E-\frac{x}{\sqrt{m}}}dx Homework Equations Actually I don't have that much experience at integrating, so could you somehow show me how to...

Homework Statement Homework Equations The Attempt at a Solution Homework Statement Homework Equations u = 1+tant du = sec^2(t) dt dt = du / sec^2(t) The Attempt at a Solution It seems like I should be using substitution in the equation, however the exponent is...

Homework Statement I want to deal with this int((5+10y^4)dy/(y+2y^5)) Homework Equations integration, substitution, partial fractions? The Attempt at a Solution I tried a bunch of random things. I think it hs to do with substitution because if I make u=y+2y^5, du/dy=1+10y^4...

Homework Statement how do i integrate v^2 / v^2 + 4 Homework Equations i understand this has something to do with arctan but if i use u substitution to let v=(u/2) so (on the bottom) it becomes (1/4)(1+(v/2)^2) there's still a v^2 on the top which the u substitution does not...

Homework Statement Integrate 1/(x2 +11x +29) Homework Equations The Attempt at a Solution I'm doing something wrong, but can't figure out what... Complete the square so that the denominator equals (x+2)2+25 Then divide by 25: ((x+2)2)/25 + 1 Move that 25 into the squared...

Homework Statement How would I begin to integrate ln(t+1) from 0 to e^2x? Homework Equations d/dx[log base a of u]=1/(lna)u du/dx Can the original equation be manipulated to use this derivative? The Attempt at a Solution Not sure where to start.

I can't figure out how to this integral. I keep coming up with the wrong answer. Can someone please show me a detailed solution?

Homework Statement Consider the Sun to be a sphere of hydrogen gas of uniform density equal to its average density (1440 kg/m3). a) Integrate the equation of hydrostatic equilibrium for dP/dr from the Sun’s radius to the core to estimate the central pressure in Pa and in atmospheres...