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artofspeed

  • 2 years ago

hard integral: http://puu.sh/23Ps6

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  1. hartnn
    • 2 years ago
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    |dw:1361078522674:dw| do you see why i did that ?

  2. artofspeed
    • 2 years ago
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    isn't this 0.5*integral of dx/(sinx+cosx)?

  3. artofspeed
    • 2 years ago
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    @Joseph91 What do you do next?

  4. Joseph91
    • 2 years ago
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    sorry error

  5. hartnn
    • 2 years ago
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    |dw:1361079028915:dw| |dw:1361079065220:dw|you know the integral of cosec ???

  6. hartnn
    • 2 years ago
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    also , did you get how its sin (x+pi/4) ??

  7. artofspeed
    • 2 years ago
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    yes and yes, thanks!

  8. hartnn
    • 2 years ago
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    that was the hint we used, for your original question, |dw:1361079880505:dw|

  9. artofspeed
    • 2 years ago
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    thanks a lot, i got it! :D

  10. hartnn
    • 2 years ago
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    welcome ^_^

  11. artofspeed
    • 2 years ago
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    I got \[\frac{1}{2\sqrt2}*\ln|\csc(2x+\pi/4)-\cot(2x+\pi/4)|\] can anyone check if it's the right answer?

  12. hartnn
    • 2 years ago
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    yes, that seems correct.

  13. artofspeed
    • 2 years ago
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    i tried to integrate on wolfram alpha, it gives me something else. To check if they are equal, I plugged a number for x in both equations, but got different answer.. :O is that normal?

  14. hartnn
    • 2 years ago
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    i think they will be equivalent, with just different form, which value you tried ?

  15. artofspeed
    • 2 years ago
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    x=-10

  16. hartnn
    • 2 years ago
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    -10 what ? degrees or radians ?

  17. artofspeed
    • 2 years ago
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    degree

  18. hartnn
    • 2 years ago
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    i checked, it comes out to be different. also i missed earlier that integral of cosec x is ln |cosec x + cot x|+c and you've typed - *minus*

  19. hartnn
    • 2 years ago
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    but our method is correct, maybe it comes different because of the constant '+c' which might be different for both forms....

  20. artofspeed
    • 2 years ago
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    hey!!! i got it, if i calculate the \[\int\limits_{a}^{b}f(x)\] of both equations, it gives the same value if a and b are the same, so it's correct! Also thanks a lot for spending so much time on this, I really appreciate it!

  21. hartnn
    • 2 years ago
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    oh, good! and welcome ^_^

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