using symmetry to calculate trig equations

hey everyone

my professor apparently gave me an exercise to calculate the integral of an equation using symmetry

the equation is:

http://www4c.wolframalpha.com/Calcul...1&w=146.&h=41.

i have no idea what this method even is eventhough is tried researching it

thanks alot for the help

Re: using symmetry to calculate trig equations

Hey ubhutto.

The attachment link seems to be broken: can you re-upload the attachment?

Re: using symmetry to calculate trig equations

the equation is the integral of

sin(x)^n / (sin(x)^n * tan(x)^n) from 0 to pi/2

sorry about that

Re: using symmetry to calculate trig equations

Wouldn't you get cancellation of the sine terms? Wouldn't that leave 1/tan(x)^n which can be written in terms of of sines and cosines?

Re: using symmetry to calculate trig equations

yup i get that but then how do i integrate that using symmetry. i don't really understand the symmetry concept because my teacher has a horrible accent. Is it possible that you can explain how to derive that. if not can you use another example to explain how to do these types of problems. thanks alot

Re: using symmetry to calculate trig equations

You actually won't be able to do the cancellation I'm thinking (since you will get a bad integral).

Have you got any examples from your class that talk about symmetry in the context of your course? Maybe if you can show us one or two, the readers can get a gist of what your teacher is getting at.

1 Attachment(s)

Re: using symmetry to calculate trig equations

Re: using symmetry to calculate trig equations

Quote:

Originally Posted by

**ubhutto** yup i get that but then how do i integrate that using symmetry.

Symmetry of an integrand is usually related to the limits of the integral. For example, we know that x^2 is an even function. That means (-x)^2 = x^2. So if we have the integral

$\displaystyle \int_0^5 x^2~dx = \frac{1}{2} \int_{-5}^5 x^2~dx$

Typically this method is used when dealing with infinities as limits of integration or trig functions.

Is this answer sufficient or do you need a more comprehensive explanation?

-Dan

Re: using symmetry to calculate trig equations

just a bit more like an explanation especially when the professor starts making x = -t and dx = -dt. why do you use dt and what is the purpose of getting the integral of f(t) + f(-t) when you can just calculate it the usual way