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anonymous

  • 5 years ago

having trouble trying to integrate sqrt (900-300(t)sqrt 2+100t^2) from 0 to 3sqrt 2

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  1. myininaya
    • 5 years ago
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    does that sqrt go over the whole thing?

  2. anonymous
    • 5 years ago
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    ya.

  3. myininaya
    • 5 years ago
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    k give me a sec let me think

  4. myininaya
    • 5 years ago
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    do you know trig substitution?

  5. anonymous
    • 5 years ago
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    ya but was having trouble tring to find the right thing to plug in

  6. myininaya
    • 5 years ago
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    =int(sqrt(100)*sqrt(t^2-3sqrt(2)t+9) =int(10*sqrt(t^2-3sqrt(2)t+9/2+9-9/2) =int(10*sqrt([t-3sqrt(2)/2)]^2+9/2) let tan pheta=[t-3sqrt(2)/2]/[3/sqrt(2)] {3/sqrt(2)} *tan pheta=t-3sqrt(2)/2

  7. myininaya
    • 5 years ago
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    {3/sqrt(2)}*sec^2(pheta) d(pheta)=dt so we have =int(10*(sqrt([9/2]tanpheta+9/2)*[3/sqrt(2)*sec^2pheta)

  8. myininaya
    • 5 years ago
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    10int(sqrt(9/2)*sqrt(tanpheta+1)*[3/(sqrt(2))]sec^2pheta) =10(3/sqrt(2))(3/sqrt(2))int(sqrt(sec^2pheta)sec^2pheta) =10(9/2)int(secpheta*sec^2pheta) =45int(sec^3pheta)

  9. myininaya
    • 5 years ago
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    is this helpful?

  10. anonymous
    • 5 years ago
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    very helpful

  11. myininaya
    • 5 years ago
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    should i go further? i havent done anything with the limits yet

  12. anonymous
    • 5 years ago
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    na i can do the limits

  13. myininaya
    • 5 years ago
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    k cool have fun

  14. anonymous
    • 5 years ago
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    thx for the help

  15. myininaya
    • 5 years ago
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    i had to complete the square above just so you know

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