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sat_chen

  • 2 years ago

verify my trigonometric substitution

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

  2. sat_chen
    • 2 years ago
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    |dw:1359525159259:dw|

  3. sat_chen
    • 2 years ago
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    |dw:1359525180291:dw|

  4. sat_chen
    • 2 years ago
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    3 dot mean continued

  5. sat_chen
    • 2 years ago
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    by the way 1/secx is cos right?

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

  7. sat_chen
    • 2 years ago
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    it should be -cot0 -0 + c

  8. sat_chen
    • 2 years ago
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    i believe

  9. dumbcow
    • 2 years ago
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    ahh right sorry

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

  11. dumbcow
    • 2 years ago
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    yw

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

  13. sat_chen
    • 2 years ago
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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

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

  15. dumbcow
    • 2 years ago
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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

  16. sat_chen
    • 2 years ago
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    ok ty

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