Intergration Definition and 65 Threads

Homework Statement A resistor of resistance 10Kohms has voltage across it described by the function V(t) = 6sin(10t+pi/4)*exp(-2t) Volts Calculate the energy dissipated in the resistor between t=0 and t=0.5 Homework EquationsThe Attempt at a Solution I have done the definite integral and have...

Hi there, Homework Statement I am doing a simulation of a free-fall lifeboat trajectory into the ocean and there is a part where i need to get the volume of the lifeboat to obtain its buoyancy force. Buoyancy force is proportional to the immersed volume of the body and this volume can be...

I cannot understand the intergration done here The part how 1/a came, what happened to the x and how did tan come into this

$$\int\frac{3x-1}{\left(3{x}^{2}-2x+1\right)^4} dx$$ $$u=\left(3{x}^{2}-2x+1\right) du=6x-2\ dx=2\left(3x-1\right)dx$$ got this far but when I tried to complete the ans was wrong the correct ans is $\frac{-1}{6\left(3x^2-2x+1 \right)^3}+C$

I know its easier to use the substitution method, by I'm trying to see how it'll work for integration by parts. I follow the LIATE method for integration by parts. Now if I take u=cos(x) and dv = sin(x), the answer changes. Can you please explain this to me? Which is the 'right'...

I am given that the equation of a curve is y = 9 / (2 - x). They then ask me to find the volume obtained by the region bounded by the curve, the coordinate axes and the line x = 1 when the region is rotated through 360° about the x-axis. My attempt: To calculate this I must use the format...

hi all, I have a TEC data and I got this TEC = \intNe ds How can I inverse this equation to get data for Ne. Thank you

Gauss Legendre numerical intergration The attachment file contain solved example i don't know how he subsitute and why a2=2 done disappear in the answer please expalin in details

Find the volume of the region inside both the sphere x^2+y^2+z^2= 4 and the cylinder (x-1)+y^2=1using cylindrical coordinates. I was thinking the inner limits would go from +(2-r) to - (2-r) the middle intervals would go from 0 to 1 and the outer limits 0 to 2pi is my approach correct

Hi, I have faced the following question. In our lab we perform different measurements on Transistors. We program a scope and that controls the tests. For one of our tests we would like to calculate the total charge Q. Mathematically this is given by Q=∫ dt i(t), where i(t) is given by i(t)...

Homework Statement S P^4 e^-P DP Homework Equations My parts. The Attempt at a Solution I know you can do u = P^4, and DV = e^-P Then, you get du = 4P^3 dx and V = -e^-P -P^4 e^P + S 4P^3 e^-p dx Now, I can just repeat that for the intergral until I get to were the P...

Homework Statement My question is mainly on the set up of the limits of the integral. The original question is: Find vector magnetic potential A distance s from a infinite long straight wire carrying DC current I. The Attempt at a Solution Let wire on z-axis and \vec I =...

Hello, What's the easiest way to evaluate an integral like this? \int_{\frac{-\pi}{2}}^{0}\cos^{10}x dx The only method I can think of is to expand the \cos^{10} x using trigonometric identities, and getting \frac{1}{32}\left(1-\cos2x\right)^5. I tried subbing u=1-\cos2x but I doesn't seem to...

Homework Statement Intergrate: \int\frac{3 dx}{\left(2-x\right)^{2}} By substituion. Homework Equations n/a The Attempt at a Solution Ok so first I take the integer out to get: 3\cdot\int\frac{dx}{\left(2-x\right)^{2}} Now I let u = 2 - x and du = dx to get...

how would i go about finding the definite integral of this (x^3*e^(x^2))/(x^2+1)^2

Hi could someone explain to me why, if I integrate dv/v between V2 and V1 the result is nastural log of V2/V1? Thanks

I have derived the following equation for the velocity of a collapsing shell of a collapsing star. \frac{dr}{dt}=-[GM(\frac{1}{2}-\frac{1}{R})]1/2 I now need to integrate this to find the free-fall time, and the hint is to manipulate the equation into a form where you can use a standard...

"Distributions" and Intergration by Parts Homework Statement Has it been proven that it is ok to use Integration by parts on "Distributions" like Dirac Delta functions inside an integration? Homework Equations Need to figure out how to write integral signs and Greek alphabet symbols...

Homework Statement \int^{4}_{2} \frac{dx}{x\left(lnx\right)^{2}} Homework Equations Let u=lnx du=\frac{1}{x}dx x=2 \rightarrow u=ln2 x=4 \rightarrow u=ln4 The Attempt at a Solution so with the u substitution we have: \int^{ln4}_{ln2} \frac{1}{u^{2}}du which goes to...

Homework Statement dy/dx = xy/(x^{2}+3y^{2}) The Attempt at a Solution I just don't know where to start. Can someone please point me in the right direction?

Homework Statement Draw a circle of radius R with the center at the origin. Get the function that represents the top half of the circle. Let d be between 0 and R. State the definite integral that gives this area. Let P be the point were x=d intersects the curve. Let theta be the angle...

Homework Statement We know the magnitude of the electric field at a location on the x-axis and at a location on the y axis, if we are far from the dipole. (a) Find \DeltaV= V_p - V_a along a line perpendicular to the axis of a dipole. Do it two ways: from superposition of V due to the two...

The integral is t(4+9t)^(1/2) dt I have tried u-sub and integration by parts but i can't figure it out. u=4+9t du=9 Does not help because i still have that t to deal with. I have spent more time then i want to admit trying to figure it out, and there are plenty more in the hw...

Homework Statement How can i determine the integration of incomplete gamma function. I mean how to determine int_0^1 gammainc(3/4,r). where gammainc(a,x)=int_0^x t^(a-1)e^(-t) dt Homework Equations The Attempt at a Solution

Homework Statement hey guys i was wondering if anyone could show my how to intergrate sqrt(x2+9). any help would be greatfully appreciated. the sqaure root is over everything:rolleyes: P.s i have looked at table of intergral but can't see one that looks similar. Homework Equations...

Really hard intergration problem\! take a look A 20-lb. monkey is attached to a 50-ft. chain that weighs 0.5 lb. per (linear) foot. The other end of the chain is attached to the 40-ft.-high ceiling of the monkey's cage. Find the amount of work the monkey does in climbing up her chain to...

Hard intergration problem! 1. A 20-lb. monkey is attached to a 50-ft. chain that weighs 0.5 lb. per (linear) foot. The other end of the chain is attached to the 40-ft.-high ceiling of the monkey's cage. Find the amount of work the monkey does in climbing up her chain to the ceiling...

Homework Statement Determine \int \int_D (x^2+y^2)dA, where D is the area in the first quadrant of the xy-plane restricted by y=0, y=x, xy=1 and x^2-y^2=1, using variable change. Homework Equations Here's a picture of the situation: http://www.aijaa.com/img/b/00050/3858610.jpg The Attempt...

Homework Statement solve by using intergration by parts x^2(cosx)dx Homework Equations My question is i got this answer but my computer algebra system gave me this answer (x^2-2)sin(x)+2xcos(x) can you tell me where i went wrong?? The Attempt at a Solution u=X^2 dv=cosx du=dx...

Homework Statement i'm taking a defitinite integral from sqrt2 to 2 of the function 1/x^3*sqrt(x^2-1)dx. Homework Equations The Attempt at a Solution I separated it into 1/x^3 and 1/sqrt(x^2-1). I have the second part using trig sub. as being sec theta dtheta, before integrating...

Homework Statement i'm taking a defitinite integral from sqrt2 to 2 of the function 1/x^3*sqrt(x^2-1)dx. Homework Equations The Attempt at a Solution I separated it into 1/x^3 and 1/sqrt(x^2-1). I have the second part using trig sub. as being sec theta dtheta, before integrating...

Homework Statement i'm taking a defitinite integral from sqrt2 to 2 of the function 1/x^3*sqrt(x^2-1)dx. Homework Equations The Attempt at a Solution I separated it into 1/x^3 and 1/sqrt(x^2-1). I have the second part using trig sub. as being inverse sec(x/1) dx. I believe i did...

I have three questions, I don't need a full working through, but I'd prefer some hints or a simmilar example for where I am going wrong/need help. The answers arn't important, but the method of working them out is. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Homework...

Homework Equations i have to find the intergral of sin squroot((x^2)+(pi^2)) The Attempt at a Solution im stuch on what i am suposed to do, i have -cos for the intergration of sin but I am confused what i do with squroot and its content.

Homework Statement \frac{dV}{dt} = 20 - kV By solving this show that V = A + Be^{-kt} Homework Equations Well I am guessing there is a ln coming into play somewhere during the intergration if the diff the bottom = the top then you get a ln(bottom) The Attempt at a Solution...

I have a question. If i have an object let say a circular cylinder buried underneath the Earth surface with X as its depth. I'm looking for the total work to plumb the oil or water that is in the cylinder to the surface if the cylinder stand virtically and has water or oil in it(Y as its...

\int\sqrt{1+x} dx = \int (u-1)\sqrt{u} du were does the 3/2 and the 1/2 come from in u ^ 5/2 /5/2 - u^ 1/2/3/2 +c

I am stuck on an intergration and can't get a simple answer which i should get p = (2*m*l^2)^(1/2)*(E+m*g*l*cos theta)^(1/2) using small angle (need for question) cos theta = 1 - (theta^2 )/2 Then I intergrate from 0 to 2*Pi and get some very large eqn using a maths program, I can't...

Evaluate the Integral: \int \frac {2x+1}{(x^{2}+9)^{2}} My attempt: \frac {2x+1}{(x^{2}+9)^{2}} = \frac {Ax+B}{x^{2}+9} + \frac {Cx+D}{(x^{2} + 9)^{2}} = (Ax+B)(x^{2} + 9)^{2} + (Cx+D)(x^{2} + 9) = Ax^{5} + Bx^{4} Dx^{3} + (18A + E)x^{2} + (81A+9D+18B)x + 9E + 81B I'm not sure what...

Homework Statement a curve has parametric equations: x = t - 2sin t y = 1 - 2cos t R is enclosed by the curve and the x axis. Show that the area of R is given by the integral: \int^{\frac{5\pi}{3}}_{\frac{\pi}{3}} (1-2\cos t)^{2} Homework Equations The Attempt at a...

Homework Statement Using the substitution u² = 2x - 1, or otherwise, find the exact value of \int^{5}_{1} \frac{3x}{\sqrt{2x-1}}dx The Attempt at a Solution Right let's rearrange u in terms of x (i think that's how you say it): x = \frac{u^{2} - 1}{2}And now get an expression for dx u =...

Homework Statement A cruve has the equation y = x{3} - 8x^{2} + 20x . The curve has stationary points A and B. There is a line through B parallel to y-axis and meets the x-axis at the point N. The region R is bounded by the curve , the x-axis and the line from A to N. Find the exact area under...

Symbolic intergration in Matlab using "INT" command? Hello, I am a bit confused a to when should we use the Symbolic intergration using "INT" command in Matlab ? Thanks

\int_{1} ^{2e} x^2(ln x)^{2} dx I need to solve this using IbP. I made the following: u = (ln x)^2 du = (\frac{2 ln x}{x}) dx dv = x^2 dx v = \frac{x^3}{3} So I get: (ln x)^2 (\frac{x^3}{3}) \|_{1} ^{2e}- \int_{1} ^{2e} (\frac{x^3}{3}) 2 ln x dx (not sure how to make...

SOme help with intergration by parts, please [b]1. Find: \int e^x cos (x) dx The Attempt at a Solution I tried using integration by parts - what we are working on... all these 3 possibilities: u = cos x, u= e^x, u = e^x cos(x) And the \int vdu are, respectively: 1. \int e^x sin(x) dx...

Evaluate the integral. \int3/(3x-2) dx from 0 to -1 (top to bottom). I change the equation to [tex(1/x - 3/2) dx[/tex] then integrated ln x-3/2x, but ln x at 0 is undefined. The textbook shows it as becoming ln (3x-2), but I'm not completely understanding how to get to that.

int^{0}_{t}[cos(sqrt{x}]dx can anyone tell me the solution to this question !

Hello, I'm having difficulty intergrating the following two functions: 1) (6x-x^2)^(-1/2) I'm fairly sure that you need to intergrate by parts for this function, but I can't figure out how to do it 2) e/(e^(2x)-1) This one I thought could do with inverse trig functions but I'm...

Homework Statement someone asked the ellipsiod problem before and i didnt under stand anythign in the repsonces >< but i had already gotten this far that my equation (simplified) is cos(theta)*sqrt[cos^2(theta) - (x^2)/(a^2)] i need to integrate this equation with respect to d(theta)...

Homework Statement Using the thechnique of multiple intergration prove that the volume of a sphere is 4/3 Pi r^3. Homework Equations The Attempt at a Solution Equation for sphere is x^2 + y^2 + z^2 = r^2 Do I solve it using for example z = root(r^2 - x^2 - y^2) Or is it...