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aprilanahi

  • 3 years ago

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

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

  2. aprilanahi
    • 3 years ago
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    cscx?

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

  4. aprilanahi
    • 3 years ago
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    I still don't get it?

  5. aprilanahi
    • 3 years ago
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    csc^2x

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

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

  8. aprilanahi
    • 3 years ago
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    So what's the answer?

  9. JamesJ
    • 3 years ago
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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

  10. aprilanahi
    • 3 years ago
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    y^2/2+2cotx+c

  11. JamesJ
    • 3 years ago
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    Double check your signs!

  12. aprilanahi
    • 3 years ago
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    Negative cotx

  13. JamesJ
    • 3 years ago
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    yes

  14. aprilanahi
    • 3 years ago
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    Yes, thank you!!!

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