Evaluating Integral of a Trigonometric Function: Homework Solution

  • Thread starter Thread starter ACLerok
  • Start date Start date
  • Tags Tags
    Integral
ACLerok
Messages
194
Reaction score
0

Homework Statement


Evaluate the integral with respect to f of the following function
http://img233.imageshack.us/img233/5303/picture1ub7.png



The Attempt at a Solution



This if for one of my homeworks. I haven't taken a single math course in almost 2 years so I'm kind of rusty. I'm not sure how to evaluate this. I tried moving the 'a' outside the integral but that doesn't help. I believe there is a trig identity I'm supposed to be able to use. Any tips or hints are greatly appreciated.
 
Last edited by a moderator:
Physics news on Phys.org
That is for the form \frac{a^2}{a^2+b^2f^2}= \frac{1}{1+ \left(\frac{bf}{a})^2}.
Does it help you to know that the derivative of arctan(x) is \frac{1}{x^2+ 1}?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Evaluating an integral of an exponential function
Replies
3
Views
1K
Please evaluate this double integral over rectangular bounds
Replies
10
Views
2K
Integrating Gravitational Attraction in n Dimensions
Replies
1
Views
2K
Can you derive a trigonometric function from its inverse dx?
Replies
9
Views
2K
Integration problem (algebraic+trigonometric function)
Replies
10
Views
1K
How Do You Prove the Fourier Transform Definition Using Integral Evaluation?
Replies
5
Views
2K
How to Solve an Integral with Trigonometric Functions and Exponents?
Replies
8
Views
2K
Integrating trig powers, why not by parts?
Replies
5
Views
2K
Delta Function Integration: Justified or Fudging?
Replies
7
Views
2K
Integrating Functions with Only One Variable for Beginners
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top