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aprilanahi

Find the indefinite integral of (y+(2/sin^2y))dy

  • one year ago
  • one year ago

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  1. JamesJ
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    Hint: what's the derivative with respect to y of cot(y) ?

    • one year ago
  2. aprilanahi
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    cscx?

    • one year ago
  3. JamesJ
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    No. But it is related to the 1/sin^2 y in your question

    • one year ago
  4. aprilanahi
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    I still don't get it?

    • one year ago
  5. aprilanahi
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    csc^2x

    • one year ago
  6. JamesJ
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    \[ \frac{d }{dy} \cot y = - \frac{1}{\sin^2 y} = - \csc^2 y \]

    • one year ago
  7. JamesJ
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    Hence \[ \int \left( y + \frac{2}{\sin^2 y} \right) \ dy = \int y \ dy + 2 \int \csc^2 y \ dy = ... \]

    • one year ago
  8. aprilanahi
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    So what's the answer?

    • one year ago
  9. JamesJ
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    You tell me. I've done the first few steps for you. You only have 2 more to do: evaluate each of those integrals above

    • one year ago
  10. aprilanahi
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    y^2/2+2cotx+c

    • one year ago
  11. JamesJ
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    Double check your signs!

    • one year ago
  12. aprilanahi
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    Negative cotx

    • one year ago
  13. JamesJ
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    yes

    • one year ago
  14. aprilanahi
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    Yes, thank you!!!

    • one year ago
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