Finding f(x) Given f''(x) and f'(x)

[kevinr]

Homework Statement

f''(x) = SQRT(x) - 2 cos(x)

What is f(x)? (all possible solutions)

Homework Equations

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The Attempt at a Solution

Well here is what i got:

f'(x) = (2/3)x^(3/2) - 2 sin(x) + C
f(x) = (2/3)(2/5)x^(5/2) + 2 cos(x) + C + D

thus final answer is:

f(x) = (4/15)x^(5/2) + 2 cos(x) + C + D

I hope that's right!

Thanks for your time! :)

 

[hotcommodity]

It's correct except for one thing. When you integrate the second time, you're integrating a constant C. What should C have after the second integration?

 

[kevinr]

Cx ?

o you thank you!