Question

If f'(x) = 3 cos (x/4) and f(pi) = 9 sqrt(2), find f(x) using integration.

Answer 1

can you write just the problem out no words?

Answer 2

http://www.wolframalpha.com use this to help you

Answer 3

@DragonSage did it help?

Answer 4

nope it gave part of the answer
this is the question:
f(x) = ∫4 sin x/4 , f(π) = 9√2
The answer is 3√2 + 12 sin (x/4)
And I want to know to how to figure it out.

Answer 5

not sure on this one sorry

Answer 6

@linda3

Answer 7

@Data_LG2

Answer 8

@BTaylor

Answer 9

anyone help? i cant figure this out

Answer 10

@ganeshie8

Answer 11

You have \(f'(x)=\cos \left( \frac{x}{4} \right)\) and have the point \( (\pi,9\sqrt{2})\).
\(f(x)\) is going to be the integral of \(f'(x)\). Can you do this part?
\[f(x) = \int\limits \cos \left(\frac{x}{4} \right) dx\]
Don't forget +C!

Answer 12

\[f(x) = -4\sin(x/8)\]

Answer 13

Oops, I forgot the 3 cos... part. Sorry. @DragonSage Can you show your work so we can help you integrate this correctly?

Answer 14

\[f(x) = 3 \cos \left(\frac{x^2}{8} \right) + c\]

Answer 15

not quite.

Answer 16

You will end up with 3(something) sin(something) + C

Answer 17

\[-3\sin((x^2/8))\]

Answer 18

almost. It will be a positive sin, since when you take the derivative of + sin you get + cos.
Have you learned about substitution?

Answer 19

isn't the derivative of cos x = -sinx ?

Answer 20

Yes, but the ANTIderivative of cos x = sin x.

Answer 21

right sorry I forgot

Answer 22

so it is \[3 \sin (x^2/8)\] , right?

Answer 23

No. You don't square the x. cos(u) is the main function. You have to multiply by 4 to compensate.

Answer 24

oh
so that makes it \[12 \sin (x/8)\]

Answer 25

where does \[3\sqrt2\] come in?