Q qqmore Member Joined Feb 8, 2007 Messages 78 Gender Undisclosed HSC 2008 Sep 28, 2008 #1 Is there a quick way to evaluate this: Integrate from 0 to pi/2 [ 1 / ( (cos x)^2 + 2(sin x)^2 ) ] otherwise the t formula will take 2 pages to write it all.....
Is there a quick way to evaluate this: Integrate from 0 to pi/2 [ 1 / ( (cos x)^2 + 2(sin x)^2 ) ] otherwise the t formula will take 2 pages to write it all.....
tommykins i am number -e^i*pi Joined Feb 18, 2007 Messages 5,730 Gender Male HSC 2008 Sep 28, 2008 #2 I'm guessing change the cos²x to 1-sin²x you get int. 1/1-s²+2s² dx = 1/1+s² dx that takes the form of an inverse tan hence evaluate [atan(sinx)]pi/2->0
I'm guessing change the cos²x to 1-sin²x you get int. 1/1-s²+2s² dx = 1/1+s² dx that takes the form of an inverse tan hence evaluate [atan(sinx)]pi/2->0
L lolokay Active Member Joined Mar 21, 2008 Messages 1,015 Gender Undisclosed HSC 2009 Sep 28, 2008 #3 divide it out by cos2x so you get sec2/(1+2tan2) = atan(rt2 tanx)/rt2 (I looked at the answer on the integrator. you should probably do that when you want to find an easier way to do something)
divide it out by cos2x so you get sec2/(1+2tan2) = atan(rt2 tanx)/rt2 (I looked at the answer on the integrator. you should probably do that when you want to find an easier way to do something)
miche11e Member Joined Jan 22, 2008 Messages 211 Location parra Gender Female HSC 2008 Sep 29, 2008 #4 i woulda done it tommykins way...
Y Yamiyo Member Joined Jul 28, 2006 Messages 146 Gender Male HSC 2008 Sep 29, 2008 #5 Tommykins' way only works if it's cosx/(cos^2(x)+2sin^2(x)) i.e. (du/dx)/(1+u^2)
