Question

Find a function F(x) satisfying F ' (x) = sin(6x).

F(x)=________

How would I start this? thanks:)

Answer 1

integrate sin(6x) with respect to x

Answer 2

could you please explain how to do that?

Answer 3

OK this is an extension of standard form

INT sin x dx = - cos x + C

INT sin (ax) dx = - cos (ax) * 1/a + C

Answer 4

hee r a = 6

Answer 5

okay, so we plug in?

sin(6x)dx= -cos(6x) * 1/6 + C ?

Answer 6

yes

Answer 7

okay:)
what happens now?

Answer 8

its usually written (-1/6) cos (6x) + C

thats F(x)

Answer 9

if you differentiate that it should give sin (6x)

Answer 10

ohh okay.. so that would be the final answer to my problem?

\[F(x)=(\frac{ -1 }{ 6 })\cos(6x) + C \] ?

if so, does C just stay like that? or does it stand for something?

Answer 11

C is the constant of integration The derivative of a constant is zero so when you do the reverse of differentiation you do not know its value or if there is a constant at all.

Answer 12

oh so what i wrote above is the final answer? just like that? (did i write it correctly?)

Answer 13

yes

Answer 14

oh okay, thank you!!