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

heydayanaBest ResponseYou've already chosen the best response.0
i 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
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
After 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,\[\large \frac{1}{4}\int\limits\limits \frac{\sec^2\theta \; d\theta}{\tan^2\theta \sqrt{\color{royalblue}{\sec^2\theta}}}\]
 one year ago

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

zepdrixBest ResponseYou've already chosen the best response.1
No 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? :)
 one year ago

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

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

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

zepdrixBest 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 \(u=\cos \theta\).
 one year ago

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

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

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

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