Find f if f''(x)=2e^t+3sin(t), f(0)=7, f(pi)=-8

- anonymous

Find f if f''(x)=2e^t+3sin(t), f(0)=7, f(pi)=-8

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- katieb

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- FireKat97

because you have been given f"(x) you need to integrate twice to get to f'(x) and then f(x)

- anonymous

I have been doing that but have not gotten the correct response

- FireKat97

Can you post your working so far?

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## More answers

- anonymous

I have quite a few different problems
But I only have one more chance to get it right.

- anonymous

Like I have worked them a lot

- FireKat97

but can you show me how you went about trying to solve the problem? So your working out so I can see where you're going wrong..

- anonymous

I am not exactly sure how to take a photo and attach a file since I am on my computer.

- FireKat97

do you think you could type up your solution?

- anonymous

its a kinda complicated solution thats why i am on here trying to get an answer for it so i an compare the correct answer to my answer to see where i went wrong

- FireKat97

okay so when you integrate 2e^x what do you get?

- anonymous

2e^x anything e^x is still e^x

- FireKat97

yup thats correct

- FireKat97

sorry what do you get when you integrate 3sint

- anonymous

-3cost

- FireKat97

Yup, thats correct too, so we know that the integral of f"(x) is 2e^t - 3cost + c

- FireKat97

so f'(x) = 2e^t - 3cost so now we have to integrate again

- anonymous

I am running out of time its an online homework due at a specific time
Can you tell me the answer? I only have one last attempt and 2/23 problems left that I have been struggling with for the past hour and a half

- FireKat97

you're not going to learn if i just tell you the answer..

- FireKat97

just try integrating f'(x) = 2e^t - 3cost + c in the same way and tell me what you get

- anonymous

The tricky part with this question is that you have two constants since you have to integrate twice
I understand the mechanics of how to do the problem and with you not telling me your answer I can't know if it is correct so if the answer you have is wrong then I am learning the wrong thing
I have tried 4 different answers so if you tell me your answer I can check to see if that was one of the answers I got

- anonymous

2e^t+3sint+cx+c

- freckles

he and you are both correct and saying
f'(x)=2e^t-3cos(t)+c
you can integrate first...
or you can use your constraint to find c...wait isn't one of your constraints written incorrectly...one of them should be f'(a)=b where a and b are some numbers ...whichever one it is use the constraint then integrate
note: if you integrate first make sure you don't use the same letter for the other constant you get after the next integration

- anonymous

But what is the final answer that you get ?

- freckles

No one can know the problem is incorrectly stated

- anonymous

What do you mean it is incorrectly stated ?

- freckles

As I was saying earlier isn't one of your constraints is suppose to be in the form f'(a)=b
where and b are some numbers?

- anonymous

yes it is supposed to be but the two questions I was stuck on do not give it in the form of f(x) and f'(x) which is why it is difficult
But it can be done
I know the steps but keep getting the wrong answer

- freckles

where a and b are some numbers*

- FireKat97

No, not necessarily.

- freckles

err...
do you not have a condition on f'?

- FireKat97

In this case, because f(0) is given, cx can be eliminated giving the constant d

- freckles

you have f(0)=7 and f(pi)=-8
one of these is really suppose to be about f'

- FireKat97

what I mean is f(x) = 2e^t - 3sint + cx + d we can find d and hence when we sub in f(pi) = -8, the value of d is already known so we can find c as well

- anonymous

no you are supposed to integrate twice fine the constant of the first integrated equation integrate again and then solve for the second constant and plug everything back into the integrated problem that gave the equation for f(x)

- FireKat97

because since f(0) = 7 is known, everything except d is equal to 0, so d = 7

- anonymous

FireKat97 that is what I have been doing and keep getting the wrong answer
Can you tell me your answer so that I can see if it is correct and then send me a picture of your work ?

- FireKat97

then we know that f(pi) = -8 = 2e^π - 3sinπ + cπ + 7 and c can now be found too

- FireKat97

I got f(x) = 2e^t - 3sin(t) + t(-15 - 2e^t)/π + 7 hoping I didn't make any silly mistakes along the way...

- freckles

I guess you guys were right about f(0)=7 and f(pi)=-8
I was just thinking they normally give a condition for each integration step
but I got a different d and c above using the conditions

- FireKat97

Unless f(0) is given, something about f'(x) is required

- freckles

right I see that now

- anonymous

the answer you gave was incorrect FireKat97

- FireKat97

do they need it in decimals if its an online quiz thing

- freckles

but yeah f(0)=7 doesn't give d=7
you should get 2-3(0)+c(0)+d=7
which this will give us a different c in the end also

- FireKat97

OH wait whoops! yeah

- anonymous

no, no decimals

- anonymous

so wait what should the answer be ?

- FireKat97

because e^0 = 1 not 0

- FireKat97

d = 5 my badddd

- anonymous

so instead of 7 it should be 5 ?

- FireKat97

yeah and so when you sub d in again for f(pi) = -8, use d as 5, so c should be different too

- anonymous

okay i give up
I just won't get points for this problem lol

- FireKat97

don't give up, you're almost there :p

- zepdrix

broski, ask for help on a question sooner than 30 minutes before the due date! XD
that's crazy sauce!

- anonymous

I still don't have an answer lol so I do not feel almost there

- anonymous

I have more than 30 minutes..

- zepdrix

For future reference, when you get into a jam like this,
https://www.wolframalpha.com/input/?i=f%27%27%28t%29%3D2e%5Et%2B3sin%28t%29%2C+f%280%29%3D7%2C+f%28pi%29%3D-8
Wolfram is really helpful with problems such as this one.
Unless your teacher considers that cheating of course :p
I find it to be a useful tool to check work though.

- zepdrix

yay \c:/

- anonymous

I have already tried wolfram and it does not work either not for this problem

- FireKat97

i copied and pasted and forgot to get fix the 5 :p haha

- zepdrix

inputting into wolfram is a little tricky :O
I think I did it correctly though, didn't i?

- anonymous

so that is not the correct answer FIREKAT?

- freckles

@Asiah321 we said d=5
and you had f(t)= 2e^t - 3sint + cx + 5 so now use this other condition f(pi) = -8
plug in pi for t and replace f(pi) wth -8 and solve for c

- freckles

oops that x should be t but whatever

- freckles

solve for c:
-8=2e^pi-3sin(pi)+c(pi)+5

- anonymous

Where is the typo ?

- Jhannybean

\[f''(x)=2e^t+3\sin(t)\]\[f'(x)=\int (2e^t+3\sin(t))dt = 2e^t-3\cos(t)+c\]\[f(x) = \int (2e^t-3\cos(t)+C)dt = 2e^t-3\sin(t) +Cx+D\]\[7=2e^{0}-3\sin(0)+C(0)+D \implies D = 5\]\[-8 = 2e^{\pi} -3\sin(\pi)+\pi C+5\]\[\pi C = -2e^{\pi}-13 \qquad \implies C=\frac{-2e^{\pi}-13}{\pi}\]\[f(x) = ....\]

- Jhannybean

Therefore, what im getting for \(f(x)\) is.. \[f(x) = 2e^{t}-3\sin(t)+\left(\frac{-2e^{\pi}-13}{\pi}\right)t+5\]

- Jhannybean

some variable errors. But you can figure out that much

- freckles

lol is it f(x) or f(t)

- Jhannybean

Haha, it's f(t).

- anonymous

Jhannybean it was correct !!!! thank you so muchhhhh !!!!

- Jhannybean

Whatever, it's f(o)

- freckles

I only wanted to point that out because there has been a bunch of mixing of variables in this post

- anonymous

jhannybean can you check your messages please

- Jhannybean

Yeah, that's why i just went with what I thought it was.

- Jhannybean

You shouldn't be thanking me, honestly. I was working it out while @freckles and @FireKat97 we're helping you solve it:P Sometimes you have to work with people instead of asking fr the answer.

- anonymous

I really appreciate you all ! I have been struggling with this problem and another one for a while

- Jhannybean

post your new question in a new thread :)

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