Question

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

Answer 1

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?

Answer 2

Tan?

Answer 3

\[Sin(2a) = 2Sin(a)Cos(a)\]

Answer 4

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

Answer 5

Not quite. In this case, a = 4t.

Sin(4t)Cos(4t) = (1/2)Sin(8t)

Answer 6

What formula or rule are you using?

Answer 7

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

Answer 8

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

Answer 9

Do a u substitution. u =8t

Answer 10

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

Answer 11

Alright, and du=8?

Answer 12

8 dt, yeah

Answer 13

then, you get ?