My aunt gave me this oldschool textbook thats older than me to work out of, and its alot harder than what im used to. I cant integrate these two functions
∫(2+3x)6dx
With upper limit 0 , lower limit -1.
and
∫(4x−1)1/3dx
upper limit 7, lower limit 1/2
Hehe sorry for my newb use of latex, on the last example the whole bracket is to the power of 1/3. I know the answers i just.. cant get them ..
make a substitution u = 2+3x change so you are integrating u w.r.t. u du/dx = 3, so dx=du/3 change the limits, so u=2+3(0) = 2 u= 2+3(-1) = -1 gives you upper limit 2, lower limit -1
make a substitution u = 2+3x change so you are integrating u w.r.t. u du/dx = 3, so dx=du/3 change the limits, so u=2+3(0) = 2 u= 2+3(-1) = -1 gives you upper limit 2, lower limit -1
giving you the integral ∫−12u63du
which should be fairly straight forward.
do the second one in the same way.
I think all that is right. I'm pretty tired.
Thank alot! Im only on C2 and didn't realise i'd be going so off track! This core mathematics book lied to me when it didnt tell me it was going to make me do stuff i didn't know
Thank alot! Im only on C2 and didn't realise i'd be going so off track! This core mathematics book lied to me when it didnt tell me it was going to make me do stuff i didn't know
Well you can just use inspection, as the other guy said. You won't really understand why that works without understanding substitution, though.
∫(ax+b)ndx u=ax+b→adu=dx Subbing in U and swapping dx for du/a gives ∫aundu which integrates to a(n+1)un+1+c Which is the formula the other poster gave, when you sub back in your f(x) for u
This is all entirely unnecessary for core 2, though. Not really sure why your teacher said they would help for that exam.
Anyway, hope some of that helped with whatever objective you're going for
Well you can just use inspection, as the other guy said. You won't really understand why that works without understanding substitution, though.
∫(ax+b)ndx u=ax+b→adu=dx Subbing in U and swapping dx for du/a gives ∫aundu which integrates to a(n+1)un+1+c Which is the formula the other poster gave, when you sub back in your f(x) for u
This is all entirely unnecessary for core 2, though. Not really sure why your teacher said they would help for that exam.
Anyway, hope some of that helped with whatever objective you're going for
I sort of understand it, this book give sthe same formula. Its just that my aunt gave me loads of books and papers to work on, but they're just titled 'Core Mathematics' and 'Pure Mathematics' so im not really sure what module im actually working on
And yeah it did help thanks, made me realise im attempting i probably wont be for almost another year
My aunt gave me this oldschool textbook thats older than me to work out of, and its alot harder than what im used to. I cant integrate these two functions
∫(2+3x)6dx
With upper limit 0 , lower limit -1.
and
∫(4x−1)1/3dx
upper limit 7, lower limit 1/2
Hehe sorry for my newb use of latex, on the last example the whole bracket is to the power of 1/3. I know the answers i just.. cant get them ..
Like others have said, these are C4. If you're doing Edexcel AS Maths, C2 integration is identical in difficulty to C1 integration but with limits and areas under curves.
Like others have said, these are C4. If you're doing Edexcel AS Maths, C2 integration is identical in difficulty to C1 integration but with limits and areas under curves.
Im ocr where we dont even meet integration until C2!