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heydayana
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{1/2}^{1} dx/ x ^{2}\sqrt{x ^{2} + 4}\]

heydayana
 one year ago
Best ResponseYou've already chosen the best response.0i got as far as \[1/4 \int\limits_{1/2}^{1} \sec ^{2}\theta/ \tan ^{3}\theta+\tan ^{2}\theta \] but im not sure what to do after

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1After you plug everything in and factor out the constants, you should have this. \[\large \frac{1}{4}\int\limits \frac{\sec^2\theta \; d\theta}{\tan^2\theta \sqrt{\color{royalblue}{\tan^2\theta+1}}}\] I'm not sure what you did on the bottom.. hmm. From here we want to use an identity, \[\large \color{royalblue}{\tan^2\theta+1=\sec^2\theta}\]Changing the integral to,\[\large \frac{1}{4}\int\limits\limits \frac{\sec^2\theta \; d\theta}{\tan^2\theta \sqrt{\color{royalblue}{\sec^2\theta}}}\]

heydayana
 one year ago
Best ResponseYou've already chosen the best response.0okay im left with \[1/4\int\limits_{1/2}^{1} \sec \theta/\sec ^{2}\theta 1 \]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1No you're left with,\[\large \frac{1}{4}\int\limits \frac{\sec \theta}{\tan^2\theta}d \theta\] You keep making weird substitutions.. I'm not sure why :c Oh you wanted it all in terms of secant I guess? :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1From here, it's probably better to convert everything to sines and cosines and the integral should be fairly simple from there :)

heydayana
 one year ago
Best ResponseYou've already chosen the best response.0yeah thats what i was trying to do. okay let me try it with sines and cosines

heydayana
 one year ago
Best ResponseYou've already chosen the best response.0still a bit confused as to what to do with the term thats squared

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large \frac{1}{4}\int\limits \frac{\sin \theta}{\cos^2\theta}d \theta\]So we get this I think? Yah it might seem a little tricky at first :) But it's just a simple `U substitution`. Let \(u=\cos \theta\).

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Woops did I set that up correctly? I was trying to do the sine and cosine conversion in my head... thinking.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Yah I did that upside down :) woops lol

heydayana
 one year ago
Best ResponseYou've already chosen the best response.0i think its cos over sin squared

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1yah good call XD whatever is on the bottom is your `u` :3
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