Recent content by Nebuchadnezza

The integral "clearly" diverges, as previously stated. you should really have made a better drawning. Oh, and perhaps you actually meant \int_{-\infty}^{\infty} \frac{1 - \cos x}{x^2} \, \mathrm{d}x ? A clever transformation, turns this integral into \int_{-\infty}^{\infty} \frac{\sin...

I am going out on a limb here, and this is probably wrong. But the one thing that comes to my mind is the fact that \int_{0}^{a} f(x) \mathrm{d}x = \int_{0}^{a} f(a-x) \mathrm{d}x For an concerete example, let us evaluate \int_{0}^{\pi/2} \frac{\sin x}{\cos x + \sin x} \mathrm{d}x I am sure...

I would use a different method, this is a complicated integral. And it is hard if not impossible to solve it using standard methods. Below is one way to evaluate it I = \int_{0}^{1} \frac{\log(t+1)}{t} \mathrm{d}t Since we are integrating over [0,1] a smart idea, is to use the maclaurin...

My main problem is that $$ e^{-ix^2} = \cos(x^2) - i \sin(x^2) $$ Whilst this integral is \cos(x^2) + \sin(x^2) . Does the minus sign change anything?

I read in some text or book that the integral \int_{-\infty}^{\infty} \cos(x^2) + \sin(x^2) \, \mathrm{d}x = \sqrt{2\pi} I was wondering how this is possible. I read on this site that one such possible way was to start by integrating e^{-i x^2} = \cos(x^2) - i \cos(x^2) My...

http://www.2shared.com/document/D6szXApS/Integrals_from_R_to_Z.html A list of my favourite integrals. https://www.physicsforums.com/showpost.php?p=3433157&postcount=272 http://www.matematikk.net/ressurser/matteprat/viewtopic.php?t=24242&postdays=0&postorder=asc&start=0...

Now, for my students and fellow teachers. I am looking to collect a great amount of problems involving factorization, and simplifications of problems. Below is a smal portion of the type of problems I am looking for. "Rules") 1) Simplify a problem, until it can not be simplified...

Could you elaborate a bit more, would one turn the loop sideways. And integrate with respect to r?

Was sitting in class thinking about this problem, did some rough sketches of a solution but never really managed to solve it. ![Ice cream cone and a loop-de-loop][1] The problem boiled down to finding out how much time the boy uses getting from the top of the loop to the bottom. Any...

Now what you could do, is write of all the nice interesting problems in your calculus book. Cut them into small papers and put them into a hat. Then you would start on the problems I gave you, when done, or mostly done. Pull a few notes from the hat. If you do not have a super memory...

http://www.2shared.com/document/D6szXApS/Integrals_from_R_to_Z.html http://www.matematikk.net/ressurser/matteprat/viewtopic.php?t=24242&postdays=0&postorder=asc&start=0 http://www.artofproblemsolving.com/Forum/resources.php?c=87&cid=184...

https://www.physicsforums.com/showpost.php?p=3433157&postcount=272 \int \sin(\ln x) + \cos(\ln x)dx \int \frac{x^2}{x^2 +4x + 8} dx \int \frac{1}{\sqrt{5x-3}+\sqrt{5x+2}} dx \int \left( x^2 + 1\right) e^{x^2}dx \int \frac{1}{\sqrt[3]{x} + x} dx The integral below is tricky, BUT it can be...

I believe strongly that this integral does not have a elementary antiderivative. Although is it possible to find an exact value for the integral below? (no approximations) I = \int_{0}^{1} \tan(x) \ln(x) \, dx

Which is exactly what I id, if you look at the post above... Here is my solution though... Never thought I would do all of it. Can anyone spot any mistakes here, as I wen through quite a lot to solve this pesky integral.

Gargl... I tried to submt this into the non homework section but alas, I was redirected here... For once this is not a problem any teacher, except the sadistic ones would give to any student. The only time you will see this integral is in the course Complex Analysis, and then you will...