August 4th, 2014, 06:55 AM  #1 
Newbie Joined: Aug 2014 From: California Posts: 3 Thanks: 0  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! 
August 4th, 2014, 06:56 AM  #2 
Newbie Joined: Aug 2014 From: California Posts: 3 Thanks: 0 
Also, I failed at using LaTeX. Sorry, not sure what I did wrong.

August 4th, 2014, 06:15 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,560 Thanks: 2561 Math Focus: Mainly analysis and algebra 
You should get a single function (without a constant) for each. First, you integrate (to find the antiderivative 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*} 
August 4th, 2014, 06:24 PM  #4 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,980 Thanks: 789 Math Focus: Wibbly wobbly timeywimey stuff.  

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