# Integration of trig functions

• Sep 9th 2008, 08:00 AM
fogel1497
Integration of trig functions
Ok so here is my integral:

INTEGRAL of [sin(5x)][cos(6x)]dx

Now this is a pretty simple u-substitution problem, i know that. Except i have one problem. The 5x and 6x inside the two trig functions is throwing me off. Is there a way to pull them apart so i just have a whole bunch of sin(x)'s and cos(x)'s? I'm stumped.
• Sep 9th 2008, 08:02 AM
Chop Suey
Use the product to sum identity:

$\displaystyle \sin{a}\cos{b} = \frac{1}{2}(\sin{(a+b)} + \sin{(a-b)})$

Then you'll get a simpler integral.
• Sep 9th 2008, 08:04 AM
fogel1497
Wow that was quick, thanks a lot. Is there a website with the list of common identities? I got through highschool calc never once talking about identities, and i get to college finding my life is useless without them.
• Sep 9th 2008, 08:05 AM
Chop Suey
Quote:

Originally Posted by fogel1497
Wow that was quick, thanks a lot. Is there a website with the list of common identities? I got through highschool calc never once talking about identities, and i get to college finding my life is useless without them.

No problem. :)

Visual Calculus - Trigonometric Identities
• Sep 9th 2008, 08:14 AM
fogel1497

-.5[ (1/11)cos(11x) + cos(-x)]

Can anyone confirm this for me?

My work is as follows:

INTEGRAL of: Sin5x * Cos6x = 1/2 * INTEGRAL of: sin(11x)+sin(-x)
by virtue of the Product sum identity

Which simplifies to -.5[ (1/11)cos(11x) + cos(-x)]
• Sep 9th 2008, 08:19 AM
Chop Suey
Quote:

Originally Posted by fogel1497

-.5[ (1/11)cos(11x) + cos(-x)]

Can anyone confirm this for me?

My work is as follows:

INTEGRAL of: Sin5x * Cos6x = 1/2 * INTEGRAL of: sin(11x)+sin(-x)
by virtue of the Product sum identity

Which simplifies to -.5[ (1/11)cos(11x) + cos(-x)]

$\displaystyle \sin{-x} = -\sin{x}$

$\displaystyle \cos{-x} = \cos{x}$

You are right.
• Sep 9th 2008, 08:45 AM
Moo
Hello,
Quote:

Originally Posted by fogel1497
Wow that was quick, thanks a lot. Is there a website with the list of common identities? I got through highschool calc never once talking about identities, and i get to college finding my life is useless without them.

Here is a website I like much : Trigonometry

The Ò is for the integral sign.

Enjoy