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August 4th, 2014, 05:55 AM   #1
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Homework Help - Antiderivatives

Find all possible functions F(\Theta) satisfying:

i)
F'(\Theta) = 4\Theta + cos\Theta
F(0) = 17

ii)
F'(\Theta) = -sin(1 - \Theta)
F(1) = 0


Hello guys, I need help with this problem. The trouble is I'm not sure what is being asked of me. More specifically I don't know whether each pair has only one function for an answer or two. Im familiar with computing antiderivatives, but this one its confusing me since its asking for a function that fits certain parameters.

I THINK the function I get for an answer should have an expression plus a constant, since anything derived from that constant would be plus zero in the antiderivative (apologies if that made no sense, I may be off in that assumption) If someone could guide me through the first one Im sure I can get the second one on my own.

Thanks in advance!
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August 4th, 2014, 05:56 AM   #2
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Also, I failed at using LaTeX. Sorry, not sure what I did wrong.
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August 4th, 2014, 05:15 PM   #3
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You should get a single function (without a constant) for each. First, you integrate (to find the anti-derivative of the given function) and then put in the given value for $\theta$ and the function, to find the value of the function for the particular solution.
$\newcommand{\d}[1]{\, \mathbb{d} #1}$
\begin{align*}
f^\prime(\theta) &= 4\theta + \cos\theta \\
\int f^\prime(\theta) \d{\theta} &= \int 4\theta + \cos\theta \d{\theta} \\
f(\theta) &= 2\theta^2 + \sin\theta + c \\
f(0) &= c = 17 \\[12pt]
f(\theta) &= 2\theta^2 + \sin\theta + 17 \\
\end{align*}
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August 4th, 2014, 05:24 PM   #4
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Quote:
Originally Posted by Taliaferro View Post
Also, I failed at using LaTeX. Sorry, not sure what I did wrong.
Wrap your code with [ math ] and [ /math ] tags.

-Dan
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