Question

integrate sqrt(cos x) with respect to x

Answer 1

pretty sure you get an elliptical integral for this one.

Answer 2

http://www.wolframalpha.com/input/?i=integrate+sqrt%28cos+x%29

Answer 3

we haven't learned what an elliptical integral is... is there any way to solve it without this knowledge

Answer 4

Let cos(x)=u

Answer 5

Then it becomes:\[\int\limits_{}^{}\sqrt{u}\]

Answer 6

or\[\int\limits_{}^{}u ^{\frac{ 1 }{ 2 }}\]

Answer 7

now just use the power rule for integrals

Answer 8

but if i integrate this how do i address the prob of chain rule

Answer 9

\[\int\limits_{a}^{b}\sqrt(u)du\]

Answer 10

\[u^(3/2)*(2/3)+C\]

Answer 11

but then, if i substitute in cos x ... \[\frac{ d }{ dx }((\cos x)^(3/2)*(2/3)+C)=\sin (x) \sqrt(\cos x)\]