Posted by Salman on Thursday, December 10, 2009 at 10:31am.
For the following integral find an appropriate trigonometric substitution of the form x=f(t) to simplify the integral.
INT((4x^23)^1.5) dx x=?

Calculus  drwls, Thursday, December 10, 2009 at 11:40am
u = 4x^2 3
(1/8)du = x dx
(1/8)INT u^(3/2) du
(1/8)(2/5)u^(5/2)
(1/20)(4x^2 3)^(5/2)
I don't see why they demand a trigonometric solution. This seems like the logical one to use.

Calculus  Anonymous, Thursday, December 10, 2009 at 4:07pm
No it is required to use a trignometric substitution. x cannot be a variable in the final answer

Calculus  Bun, Thursday, December 10, 2009 at 5:51pm
you can do like this:
(4x^23)^1.5 = (4x^23).sq(4x^23)dx
Let 2x = Sq3.sec(det)
so, 4x^2 3 = 3.sec^2(det)3
= 3.tan^2(det)
new INT= INt(3^1.5tan^3(det)d(det)
Use Pythagore to solve the relation between x and the angle det.
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