Question

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

Answer 1

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

Answer 2

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

Answer 3

Can you post your working so far?

Answer 4

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

Answer 5

Like I have worked them a lot

Answer 6

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..

Answer 7

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

Answer 8

do you think you could type up your solution?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

yup thats correct

Answer 13

sorry what do you get when you integrate 3sint

Answer 14

-3cost

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

2e^t+3sint+cx+c

Answer 22

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

Answer 23

But what is the final answer that you get ?

Answer 24

No one can know the problem is incorrectly stated

Answer 25

What do you mean it is incorrectly stated ?

Answer 26

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?

Answer 27

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

Answer 28

where a and b are some numbers*

Answer 29

No, not necessarily.

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

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)

Answer 35

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

Answer 36

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 ?

Answer 37

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

Answer 38

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...

Answer 39

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

Answer 40

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

Answer 41

right I see that now

Answer 42

the answer you gave was incorrect FireKat97

Answer 43

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

Answer 44

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

Answer 45

OH wait whoops! yeah

Answer 46

no, no decimals

Answer 47

so wait what should the answer be ?

Answer 48

because e^0 = 1 not 0

Answer 49

d = 5 my badddd

Answer 50

so instead of 7 it should be 5 ?

Answer 51

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

Answer 52

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

Answer 53

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

Answer 54

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

Answer 55

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

Answer 56

I have more than 30 minutes..

Answer 57

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.

Answer 58

yay \c:/

Answer 59

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

Answer 60

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

Answer 61

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

Answer 62

so that is not the correct answer FIREKAT?

Answer 63

@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

Answer 64

oops that x should be t but whatever

Answer 65

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

Answer 66

Where is the typo ?

Answer 67

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

Answer 68

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

Answer 69

some variable errors. But you can figure out that much

Answer 70

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

Answer 71

Haha, it's f(t).

Answer 72

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

Answer 73

Whatever, it's f(o)

Answer 74

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

Answer 75

jhannybean can you check your messages please

Answer 76

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

Answer 77

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.

Answer 78

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

Answer 79

post your new question in a new thread :)