Recent content by AndersCarlos

Bearded Man: Yes, I have almost no homework. I already put some quite time in studying, I get some harder books, and try to study, however I get a little demotivated when I see that there are some students that put a lot of efforts in studying for the same admission and have the school to...

Well, it would be a long story, but I'll try to make it shorter: I could somehow say that there are two types of admissions in a public university in my country. "Traditional" and a new model recently approved by the government, which could be compared to SAT. I intend to enter a university...

Well, people get exhausted from studying continuously, which can eventually lead to death. It is indeed very rare for someone to reach this point of exhaustion, but it happens. Isaac Newton supposedly was able to study/work 16~18 hours per day and sleep for 3~4 hours. He didn't die due to all...

micromass and Curious3141: Well, I chose that: 2x = π/2 - u then, dx = -du/2 \int_{0}^{\frac{\pi}{2}} sin^m (2x)dx = - \int_{\frac{\pi}{2}}^{\frac{-\pi}{2}} \frac{sin^m (\frac{\pi}{2} - u)}{2}du = \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \frac{cos^m (u)}{2} du = \int_{0}^{\frac{\pi}{2}} cos^m...

micromass: cos x

micromass: Using the Pythagorean trigonometric identity. Well, this would become (if I take the positive root): sin^m 2x = (1-cos^2 2x)^{\frac{m}{2}} I'm trying 'u' = cos x this time.

Homework Statement I've been solving a problem, the solution is complete, however, I must prove that the following relation is true: \int_{0}^{\frac{\pi}{2}} sin^m 2x dx = \int_{0}^{\frac{\pi}{2}} cos^m x dx for any m. Homework Equations - The Attempt at a Solution Well, I've trying to...

SammyS: Finally I was able to get it correctly, thank you very much.

Sorry, forgot to put the 'n' exponent. I would put the (n-1) exponent, but tex shows it wrongly... x^(n-1) So, where should I expand the factor? The initial integral or the one after the integration by parts? Sorry, for not understanding, but in what does expanding the factor will help?

Well, it became this: x(a^2 - x^2) + \int \frac{2nx(a^2 - x^2)^ndx}{(a^2-x^2)} So I took 2n out of the integral, as it's constant, then, I've tried using: u = (a^2 - x^2)^(n-1) and dv = x, which will result in another integral: ∫nx^3(a^2 - x^2)^(n-2)dx, so this way will just generate (n-k)...

Homework Statement Use integration by parts to derive the formula: \int (a^2 - x^2)^n dx = \frac{x(a^2-x^2)^n}{2n+1} + \frac{2a^2n}{2n+1}\int \frac{(a^2 - x^2)^n}{(a^2 - x^2)} dx + C Homework Equations Integration by parts general formula ∫udv = uv - ∫vdu The Attempt at a...

Curious3141: Ah, I just saw what went wrong. When I was solving it and went to the next line, I forgot to write the minus sign inside the integral, that's why I got the wrong intervals. Thank you again.

Curious3141: Just a little question (A edit would be better, but I don't know if you would see it). If I have another problem, should I create a new thread or can I post it in this one?

I was just finishing the proof that 1/(1+x^2) is even. I got the following result: \frac{\pi}{2}(\int_{0}^{1} \frac{du}{1+u^2} + \int_{0}^{-1} \frac{du}{1+u^2}) Then I used the property of even functions so this would become: \frac{\pi}{2}(2\int_{0}^{1} \frac{du}{1+u^2}) Then, according to...

Curious3141: After some seconds, I could get the right answer for part a, thank you very much. About part b, well, I just double-checked both Spanish and English versions of Apostol. Both show the question as I've written.