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anonymous
 4 years ago
Integrate
anonymous
 4 years ago
Integrate

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{\pi/2}\sqrt{1+\cos t}dt\] \[\int\limits_{0}^{\pi/2}\sqrt{1+\sin t}dt\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Do you know that 1+cost= 2cos^2 (t/2) ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0No, where did that identity come from?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ok lets see do you know cos 2x= 2cos^2 x1. ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so take 1 to the other side you get 1+ cos 2x= 2cos^x. Replace 2x by x. You get 1+ cos x= cos^x/2.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0There a 2 on the RHS.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I meant that 1= cos x =2 cos^x/2. I forgot the 2 in the earlier post. RHS means right hand side lol.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Okay, I'll try to integrate it. So, the same goes for the sin one?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The two integrals are equal. And that is not an identity for sine.Only for cos. If you want to do the sin then 1+sinx= (sin (x/2) + cos(x/2))^2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I got an answer of 2 for the cosine one?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Where did the sin identity come from?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Well expand the RHS and you get sin ^ x/2 + cos^2 x/2 + 2sin (x/2)cos(x/2) . sin ^2 x/2+ cos ^2 x/2=1. and 2sinx/2 cosx.2=sin x. So it becomes 1+sin x.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Do you know the property. \[\int\limits_{0}^{a}f(x)= \int\limits_{0}^{a}f(ax)\]. If you apply this property then the second integral becomes the first one. So you don't need to do thhe second one it is equal to the first one.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ah, I didn't know this property. I'm going to write it down. But how did you find the sin identity. I understand the reverse and it works but how did you think it up?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Well its standard formula you just need to know it... :P

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0It's not written anywhere in my textbooks. :(
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