Edexcel integration questions a level
https://imgur.com/a/Zc8Aslz
Could anyone help me with this question please? My working out is above as is the question and I end up getting ln 9/7 as the answer. The book says ln 7/3 but I can’t see what I’ve done wrong.
Could anyone help me with this question please? My working out is above as is the question and I end up getting ln 9/7 as the answer. The book says ln 7/3 but I can’t see what I’ve done wrong.
Reply 1
21
Original post
by username79352https://imgur.com/a/Zc8Aslz
Could anyone help me with this question please? My working out is above as is the question and I end up getting ln 9/7 as the answer. The book says ln 7/3 but I can’t see what I’ve done wrong.
Could anyone help me with this question please? My working out is above as is the question and I end up getting ln 9/7 as the answer. The book says ln 7/3 but I can’t see what I’ve done wrong.
The ans is ln(9/7).
https://www.wolframalpha.com/input?i=integrate+1%2F%281%2Be%5Ex%29+from+ln%282%29+to+ln%286%29
Reply 2
Original post
by mqb2766Oh phew ok thank you!
Reply 3
21
Original post
by username79352Oh phew ok thank you!
Youve done it the right way, but by "adding 0" to the numerator you could have written the integrand as
(1 + e^x - e^x ) / (1 + e^x) = 1 - e^x/(1+e^x)
and the indefinite integral is then
x - ln(1+e^x) + c = ln(e^x/(1+e^x)) + c
which gives the same result when subbing in ln(6) and ln(2) for x. So a couple of lines to do the integration, then a couple more to evaluate the limits.
Its part about guessing that the result is going to be somehting like ln(1+e^x), then thinking about how you can get a f'(x) on the numerator.
(edited 1 year ago)
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