Question

what is the antiderivative of cos((1/3)*theta)

Answer 1

what do you mean by antierivative ?
if you differentiate its -1/3 sin(1/3 theta)
if you integrate its 3 sin (1/3 theta)

Answer 2

integrate is what i meant. How is it times 3. The 3 is the only thing i dont know where it comes from

Answer 3

here the trick. you substitute 1/3 theta = x
so u get cos (1/3 theta) (d theta) = cos x d (3 x) = 3 cos x dx = 3 sin x = 3 sin 1/3 theta

Answer 4

on this section I cant use substitution yet.

Answer 5

i guess substitution is the only way to explain, or else, you have to go by first principles which is more difficult.

Answer 6

airight thanks