# Thread: Integration of trig functions

1. ## 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.

2. 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.

3. 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.

4. 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

5. For my answer I got:

-.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)]

6. 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.

7. Hello,
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