The integrand = -2x * 'rubbish'
Hey,
I have this question:
My book says to use the substition
Using that substition i get a du that is some utter rubbish and couldn't help in solving this.
If i use u = 3-x instead i get an answer but it's still wildly different from the books.
How could i use the u^2 substitution?
Thanks
ARGHH - i've really got to stop making this rookie mistakes!! Very sorry!
so...
becomes...
And finally i get:
If thats right, how does that go back into the function. usually i have just a constant to take outside the integral. Sorry for all the questions.
Thanks
No prob. Again, all you need do is express -2x in terms of u then integrate with respect to u. I suppose someone may fill in the whole story. I'll add a pic in a couple of mins.
Here we are. Just in case a picture helps...
i.e...
... where
... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).
Spoiler:
__________________________________________
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!
You'll find this place integrate x/sqrt(3 - x) - Wolfram|Alpha useful and if you click on 'show steps' you'll see that yes the two answers are equivalent. (Interestingly, they haven't used quite the same u.)
Oh gosh don't worry about my crazy method! Whatever works for you.