anonymous
  • anonymous
integrate using trig sub. problem below.
Calculus1
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[\int\limits_{1/2}^{1} dx/ x ^{2}\sqrt{x ^{2} + 4}\]
amoodarya
  • amoodarya
put x=2tan u
anonymous
  • anonymous
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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

zepdrix
  • zepdrix
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,\[\large \frac{1}{4}\int\limits\limits \frac{\sec^2\theta \; d\theta}{\tan^2\theta \sqrt{\color{royalblue}{\sec^2\theta}}}\]
anonymous
  • anonymous
okay im left with \[1/4\int\limits_{1/2}^{1} \sec \theta/\sec ^{2}\theta -1 \]
zepdrix
  • zepdrix
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? :)
zepdrix
  • zepdrix
From here, it's probably better to convert everything to sines and cosines and the integral should be fairly simple from there :)
anonymous
  • anonymous
yeah thats what i was trying to do. okay let me try it with sines and cosines
anonymous
  • anonymous
still a bit confused as to what to do with the term thats squared
zepdrix
  • zepdrix
\[\large \frac{1}{4}\int\limits \frac{\sin \theta}{\cos^2\theta}d \theta\]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
  • zepdrix
Woops did I set that up correctly? I was trying to do the sine and cosine conversion in my head... thinking.
zepdrix
  • zepdrix
Yah I did that upside down :) woops lol
anonymous
  • anonymous
i think its cos over sin squared
zepdrix
  • zepdrix
yah good call XD whatever is on the bottom is your `u` :3
anonymous
  • anonymous
okay thanks a lot!

Looking for something else?

Not the answer you are looking for? Search for more explanations.