A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Help with a few calc II problems for Trigometric Substitution? 10 | (100-x^2)^(1/2) dx 5 I have 6 others I am struggling with but I figured start one at a time. Thanks in advance.

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits_{5}^{10} \sqrt{100-x^2}dx\] for a better version of the problem

  2. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Make the substitution of \(\sin \theta = \frac {x}{10} \) \(10\cos \theta d\theta = dx \) \[\int \limits_5^{10} 10\sqrt{1-(x/10)^2}dx = \int \limits_{0.5}^{1} 10\sqrt{1-\sin^2\theta}(10\cos \theta )d\theta\]

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That much I got.

  4. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    tell us where is the problem then?

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, I don't know where to go from here. I've been struggling with trigometric problems since day 1 and this is so far the most obnoxiously difficult. Also I converted b and a into radians.

  6. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[100\cos \theta\sqrt{1-\sin^2\theta}= 100\cos^2 \theta\] The integral is finally sum up to- \[100\int\limits_{0.5}^{1}\cos^2\theta d\theta \] use double angle identity to replace \(\cos ^2\theta \) to \(\cos (2\theta)\)

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok. so \[100\int\limits_{.5}^{1}\cos2 \theta d \theta. \] And from there? I'm really sorry, I have no idea what I'm doing with these. I just know the answer is supposed to be 25(2pi/3 - sqrt3/2)

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.