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dfresenius
 2 years ago
Trig integrals. sqrt(1cos2x)dx
dfresenius
 2 years ago
Trig integrals. sqrt(1cos2x)dx

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dfresenius
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1360952276270:dw

dfresenius
 2 years ago
Best ResponseYou've already chosen the best response.0should i do a u sub or change cos2x identity?

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.2Well, cos(2x) = cos^2 x  sin^2 x = 1  2sin^2 x, hence \[ \sqrt{1  \cos 2x} = \sqrt{1  (1  2\sin^2 x)} \] which can be nicely simplified.

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.2What does this expression simplify to? \[ \sqrt{1  \cos 2x} = \sqrt{1  (1  2\sin^2 x)} \]

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.2\[ \sqrt{1  (1  2\sin^2 x)} = \sqrt{2\sin^2 x} = ... \]

dfresenius
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1360954273501:dw

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.2\[ \sqrt{1  (1  2\sin^2 x)} = \sqrt{2\sin^2 x} = \sqrt{2} \sin x \] provided sin x > 0. Hence \[ \int \sqrt{1  \cos 2x} \ dx \ = \ \int \sqrt{2} \sin x \ dx \ = \ ... \]

dfresenius
 2 years ago
Best ResponseYou've already chosen the best response.0from 0 to pi, the book asnwer says its 2sqrt2

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.2What is cos(pi) = ...? And cos(0) = ... ?

dfresenius
 2 years ago
Best ResponseYou've already chosen the best response.0sqrt(2) + sqrt(2) oh ya 2sqrt 2

dfresenius
 2 years ago
Best ResponseYou've already chosen the best response.0sorry for wasting your time :(
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