Homework Help - Antiderivatives

[Taliaferro]

Find all possible functions F(~) satisfying:

i)
F'(~) = 4(~) + cos(~)
F(0) = 17

ii)
F'(~) = -sin(1 - ~)
F(1) = 0

*[ ~ = theta ]*

Hello all, 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.

We haven't had a problem specifically like this is class but from my notes 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 at least could guide me through the first one I'm sure I can get the second one on my own.

 

[Deleted member 4993]

Find all possible functions F(~) satisfying:

i)
F'(~) = 4(~) + cos(~)

F(Θ) = 2(Θ)² + sin(Θ) + C₁ ...................Now continue...

F(0) = 17

ii)
F'(~) = -sin(1 - ~)

F'(Θ) = - sin(1-Θ)

F(Θ) = cos(1-Θ) + C₂ ...................Now continue...

F(1) = 0

*[ ~ = theta ]*

Hello all, 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.

We haven't had a problem specifically like this is class but from my notes 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 at least could guide me through the first one I'm sure I can get the second one on my own.

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Why didn't you show those antiderivatives - then we could have progressed further!!

 

[Taliaferro]

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Why didn't you show those antiderivatives - then we could have progressed further!!

Lol, I didnt know where to begin.

So I'd like to be sure I can describe in words what is going on here. Please correct me where I'm wrong, because the vocabulary kind of jumbles together in my brain. What you did just now, was that you taking the antiderivatives of
F'(Θ) = 4(Θ) + cos(Θ) and F'(Θ) = -sin(1 - Θ) ? Because you worked backwards, in a sense?


Now, Im sorry, but I still dont understand what I'm supposed to do from here. I know that F(0)= 17 is the area under the function at point (0, 17), right? But I admittedly do not understand trig functions very well. My confusion now stems from what F(Θ) = 2(Θ)² + sin(Θ) + C₁and F(Θ) = cos(1-Θ) + C₂ I are supposed to mean to me. They are integrals so I assume they are also points on the graph with an area under them as well?

Im not sure what the value of theta is supposed to be. Is it zero? and the values of cos(0)= 1 , sin(0)= 0
Is theta supposed to be = 1 in the second part.
That is my thought process, lol, still a little confused and thank you for helping me!

 

[Taliaferro]

I hope its ok if I bump this. I really need to understand how to do these two problems for my final later today.