Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Denebel

  • 2 years ago

Use the given trig identity to set up a u-substitution and then evaluate the indefinite integral.

  • This Question is Closed
  1. Denebel
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1326790438109:dw|

  2. FoolForMath
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Yes, where are you stuck?

  3. imperialist
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Hint: what is the derivative of tan(x)?

  4. Denebel
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    How to start? Can I do this ? |dw:1326790556349:dw|

  5. Denebel
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Derivative of tan x is (sec x)^2

  6. imperialist
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, so try only breaking one of the (sec x)^2 into 1+(tan x)^2

  7. imperialist
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You will be pleasantly surprised!

  8. FoolForMath
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[ \int \sec^4 x \space dx = \int (1+\tan^2 x) \sec^2 x \space dx \]

  9. FoolForMath
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Now put \( \tan x = z \implies \sec^2 x dx = dz \)

  10. FoolForMath
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    So, \[ \int (1+\tan^2 x) \sec^2 x \space dx = \int (1+z^2) dz \] I am sure you can proceed after this.

  11. Denebel
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh I see now. Thank you very much!

  12. FoolForMath
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Glad to help :)

  13. imperialist
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Likewise :)

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.