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Trigonometric Integration

Yuuki

Member
Jun 7, 2013
43
how do i integrate sin(pi*x)*sqrt(1 + pi*2*cos(pi*x)^2)?
i reduced this to sqrt(u^2-u) but i don't know how to go from here
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: integration

I think what you have written should be interpreted as:

\(\displaystyle \int \sin(\pi x)\sqrt{1+2\pi\cos^2(\pi x)}\,dx\)

Is this correct? And if so, what substitution did you use?
 

Prove It

Well-known member
MHB Math Helper
Jan 26, 2012
1,403
Re: integration

how do i integrate sin(pi*x)*sqrt(1 + pi*2*cos(pi*x)^2)?
i reduced this to sqrt(u^2-u) but i don't know how to go from here
Substitute [tex]\displaystyle \begin{align*} u = \cos{ \left( \pi \, x \right) } \implies du = -\pi\sin{ \left( \pi \, x \right) } \, dx \end{align*}[/tex] to start with...
 
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