- #1
Nikarasu M
- 17
- 0
Hello,
Say I'm working with ∫ sqrt(1-cos(t)) dt
I end up with a substitution of u = 1-cos(t) and dt = du/sin(t)
sub back in: ∫ sqrt(u) / sin(t) du
Still got a t in there ... hrrmmm
So I go to wolfram alpha for some inspiration and 'show steps':
http://www.wolframalpha.com/input/?i=integrate++sqrt(1-cos(t))
After some bashing about I see what they are doing is valid - but have no idea how to go about spotting what they have done in between the substitution and ending up with an integral only in terms of u.
I need a little sub-'show-working' section - anyone care to show me how the 'ah-hah, that'll work!' moment actually comes about ?
It's simple ?
regards,
N
Say I'm working with ∫ sqrt(1-cos(t)) dt
I end up with a substitution of u = 1-cos(t) and dt = du/sin(t)
sub back in: ∫ sqrt(u) / sin(t) du
Still got a t in there ... hrrmmm
So I go to wolfram alpha for some inspiration and 'show steps':
http://www.wolframalpha.com/input/?i=integrate++sqrt(1-cos(t))
After some bashing about I see what they are doing is valid - but have no idea how to go about spotting what they have done in between the substitution and ending up with an integral only in terms of u.
I need a little sub-'show-working' section - anyone care to show me how the 'ah-hah, that'll work!' moment actually comes about ?
It's simple ?
regards,
N
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