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sat_chen

verify my trigonometric substitution

  • one year ago
  • one year ago

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  1. sat_chen
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    integral of ((sqrt(4-x^2)/x^2)dx

    • one year ago
  2. sat_chen
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    |dw:1359525159259:dw|

    • one year ago
  3. sat_chen
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    |dw:1359525180291:dw|

    • one year ago
  4. sat_chen
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    3 dot mean continued

    • one year ago
  5. sat_chen
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    by the way 1/secx is cos right?

    • one year ago
  6. dumbcow
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    ok sorry about delay...heres what your steps should be \[x = 2\sin \theta\] \[dx = 2\cos \theta d \theta\] \[\rightarrow \int\limits_{}^{} \frac{2 \cos \theta}{4 \sin^{2} \theta} (2 \cos \theta) d \theta\] \[= \int\limits_{}^{}\frac{ \cos^{2} \theta}{\sin^{2} \theta} d \theta \] \[=\int\limits_{}^{}\frac{1-\sin^{2} \theta}{\sin^{2} \theta} d \theta\] \[=\int\limits_{}^{} \csc^{2} \theta - 1\] \[= \cot \theta - \theta +C\]

    • one year ago
  7. sat_chen
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    it should be -cot0 -0 + c

    • one year ago
  8. sat_chen
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    i believe

    • one year ago
  9. dumbcow
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    ahh right sorry

    • one year ago
  10. sat_chen
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    and yep i did the same steps as you ty a lot for your help

    • one year ago
  11. dumbcow
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    yw

    • one year ago
  12. sat_chen
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    and thanks a lot for taking time to clear my confusions

    • one year ago
  13. sat_chen
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    and you did in so many fewer steps then me going have to start doing it in my head as well

    • one year ago
  14. sat_chen
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    can i message you later if i have more questions in my homework :)

    • one year ago
  15. dumbcow
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    sure thing ... and i did skip some steps just for sake of time and space, but on paper its good to be thorough so you don't make any mistakes

    • one year ago
  16. sat_chen
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    ok ty

    • one year ago
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