Please help me solve this problem (Integration of Trig. function).

**ronaldkaka** · May 7th 2009, 05:28 PM

I'm very new for calculus.
please solve this problem. thank you very much.

**Banned for attempted hacking** · May 7th 2009, 05:33 PM

Originally Posted by ronaldkaka

I'm very new for calculus.
please solve this problem. thank you very much.

Multiply top and bottom by ( sin^7 x - cos ^7 x)

you get on the bottom sin^14 x - cos^14 x

cos^2 x = 1 -sin^2x

Use this identity then finish of the question.

**ronaldkaka** · May 7th 2009, 06:01 PM

Thank you very much Mr.╔(σ_σ)╝.
But please describe more.

**Banned for attempted hacking** · May 7th 2009, 07:28 PM

Originally Posted by ronaldkaka

Thank you very much Mr.╔(σ_σ)╝.
But please describe more.

I gave you a useless step, sorry i wasn't thinking about it.

Anyway i'm going to suggest something radical and an easy way out.

But i'm not sure if you are allowed to leave your answers in terms of non elementary fuctions.

Divide everything by cos^7 x

you get $\frac{tan^{7} x}{ 1 + tan^{7} x} = 1 - \frac{1}{1 + tan^{7}x}$

use a substitution u = tanx

du = sec^2 x = ( u^2 - 1)

you get

$\frac{1}{ (u^{2} -1)( 1+u^{7})}$ you can do this

$\frac{1}{(u-1)(u+1)(1+u^{7})}$

Partial fractions would be appropriate.

If you get something like

$\frac{Au+b}{(1+u^{7})}$

You may have to use the maclaurin series or do some more algrabra. I didn't try it so i'm not sure what you would end up with.

Good luck though. The algebra seems disgusting.

I popped it into an online integrator and it doesn't look pretty.
Wolfram Mathematica Online Integrator

**ronaldkaka** · May 7th 2009, 07:39 PM

Great.
Thank you very much ╔(σ_σ)╝.

**Banned for attempted hacking** · May 7th 2009, 07:52 PM

I think you might get stuck with the partial fraction.

$\frac{1}{(u^{2}-1)(u^{7} +1)}$ =

$\frac{-3x^{4}+2x^{3} -4x^{2} +2x -3}{7( x^{6}-x^{5}+x^{4} -x^{3} +x^{2}-x +1)} + \frac{1}{4(x-1)}- \frac{1}{4(x+1)} - \frac{1}{14(x+1)^{2}}$

Did it with pc.

Forget about this integral; it's not the kind of thing you would see in an exam.

**NonCommAlg** · May 7th 2009, 09:34 PM

Originally Posted by ronaldkaka

I'm very new for calculus.
please solve this problem. thank you very much.

it's a very standard integral: do the substitution $x \to \frac{\pi}{2} - x$ and then add the two integrals together to get $\int_0^{\frac{\pi}{2}} dx=\frac{\pi}{2}.$ so the value of the integral is $\frac{\pi}{4}.$

Thread: Please help me solve this problem (Integration of Trig. function).

LinkBack

Thread Tools

Display

Please help me solve this problem (Integration of Trig. function).

Similar Math Help Forum Discussions

Compute Trig Function Values, Solve Trig Equation

Integration of trig function

integration by parts/ inverse trig function

another integration with substitution of trig/hyperbolic function

integration with substitution of trig/hyperbolic function

Search Tags