Integration help
Help… for these type of qs can I leave my answer as +c instead of the +k ??
(edited 10 months ago)
Yes any constant is fine
Original post by Alevelhelp.1
Help… for these type of qs can I leave my answer as +c instead of the +k ??
If your working is this
ln(y) = ln(x+1) + C
And then your final answer is
Y = C(x+1)
Then you’re saying that both Cs are the same value but they are not.
Since your final answer by itself is right, you won’t lose marks in an exam if you only use C in your working but it’s always good to have correct and clear working.
The working in full would look like this although you don’t need to write all the steps if you’re confident with this process:
ln(y) = ln(x+1) + C
ln(y) = ln(x+1) + ln(K)
ln(y) = ln(K(x+1))
y = K(x+1)
Original post by Notnek
If your working is this
ln(y) = ln(x+1) + C
And then your final answer is
Y = C(x+1)
Then you’re saying that both Cs are the same value but they are not.
Since your final answer by itself is right, you won’t lose marks in an exam if you only use C in your working but it’s always good to have correct and clear working.
The working in full would look like this although you don’t need to write all the steps if you’re confident with this process:
ln(y) = ln(x+1) + C
ln(y) = ln(x+1) + ln(K)
ln(y) = ln(K(x+1))
y = K(x+1)
ln(y) = ln(x+1) + C
And then your final answer is
Y = C(x+1)
Then you’re saying that both Cs are the same value but they are not.
Since your final answer by itself is right, you won’t lose marks in an exam if you only use C in your working but it’s always good to have correct and clear working.
The working in full would look like this although you don’t need to write all the steps if you’re confident with this process:
ln(y) = ln(x+1) + C
ln(y) = ln(x+1) + ln(K)
ln(y) = ln(K(x+1))
y = K(x+1)
Thanks
but for qs where we don’t need to put an ln|x| (natural log)
Do I still but k or is c fine because there’s no logs
Original post by Alevelhelp.1
Thanks
but for qs where we don’t need to put an ln|x| (natural log)
Do I still but k or is c fine because there’s no logs
but for qs where we don’t need to put an ln|x| (natural log)
Do I still but k or is c fine because there’s no logs
You can use any letter to show a constant. My point was that if you have two different constants in your working then you should be using two different letters. In the example above you could have used any letters e.g. A.
“For qs where we don’t…”
Do you have an example of a question like this?
A small observation about the above is you should have abs in the log argument as in
ln(|x|) = ...
Its related to the constants etc as in
dx/dt = 2x
x(0) = -1
so the solution is obviously x(t) = -e^2t, but working it through without abs youd get to
ln(x) = 2t + c
Note that ln(x) doesnt exist as x is negative and taking exponentials you get
x(t) = e^c e^2t = Ae^2t
If you left it in terms of c, the initial condition of -1 "doesnt work" as you cant get a c which satisfies it (e^c > 0). Trivially though A=-1 works. If you used the abs properly.
ln(|x|) = 2t + c
Then youd have to consider x>0 and x<0 seperately and the latter does give a valid c. However, in both cases Ae^2t works where A is the (transformed) constant of integration.
So if you leave it as +c, make sure you have abs in the log, otherwise it could be incorrect. However, putting it as Ae^2t is simpler, where A can be either positive or negative, though Notnek is better placed to say whether youd lose a mark or not.
ln(|x|) = ...
Its related to the constants etc as in
dx/dt = 2x
x(0) = -1
so the solution is obviously x(t) = -e^2t, but working it through without abs youd get to
ln(x) = 2t + c
Note that ln(x) doesnt exist as x is negative and taking exponentials you get
x(t) = e^c e^2t = Ae^2t
If you left it in terms of c, the initial condition of -1 "doesnt work" as you cant get a c which satisfies it (e^c > 0). Trivially though A=-1 works. If you used the abs properly.
ln(|x|) = 2t + c
Then youd have to consider x>0 and x<0 seperately and the latter does give a valid c. However, in both cases Ae^2t works where A is the (transformed) constant of integration.
So if you leave it as +c, make sure you have abs in the log, otherwise it could be incorrect. However, putting it as Ae^2t is simpler, where A can be either positive or negative, though Notnek is better placed to say whether youd lose a mark or not.
(edited 10 months ago)
Quick Reply
Related discussions
- Help urgent maths
- Help maths urgent ‼️
- essay question
- Integrated masters
- Mechanics help
- Help with differential equations please.
- A Level maths mechanics help
- Help integration
- Maths Integration
- Maths: Integration
- Need help with some Alevel business multiple choice question
- A level maths mechanics question (1)
- Applied Calculus Help
- Integration question
- Help I don’t understand integration
- Funding 2nd degree part-time eligibility
- KCL acceptance through foundation year!
- Integration
- A-level Maths, Integration, Finding area between curves & Lines.
- Need help with Integration
Latest
Trending
Last reply 4 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
Trending
Last reply 4 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
