What is the anti derivative of sin(4t)cos(4t) and what method would you use?

Question

anonymous · Answer

First, we can simplify the expression. You can use a trig identity to combine the sine and cosine into a single trig function. Does it remind you of any particular identity?

anonymous · Answer

Tan?

anonymous · Answer

$$Sin(2a) = 2Sin(a)Cos(a)$$

anonymous · Answer

so, Sin(4t)Cos(4t) = 4sin(t)cos(t)?

anonymous · Answer

Not quite. In this case, a = 4t.

Sin(4t)Cos(4t) = (1/2)Sin(8t)

anonymous · Answer

What formula or rule are you using?

anonymous · Answer

Half angle formula for sine (or double angle, something like that, I forget the name)

anonymous · Answer

so, what do you do after you get Sin(4t)Cos(4t) = (1/2)Sin(8t)

anonymous · Answer

Do a u substitution. u =8t

anonymous · Answer

If I'm saying anything that you haven't heard about at this point, let me know.

anonymous · Answer

Alright, and du=8?

anonymous · Answer

8 dt, yeah

anonymous · Answer

then, you get |dw:1398912854078:dw|?