anonymous
  • anonymous
having trouble trying to integrate sqrt (900-300(t)sqrt 2+100t^2) from 0 to 3sqrt 2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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myininaya
  • myininaya
does that sqrt go over the whole thing?
anonymous
  • anonymous
ya.
myininaya
  • myininaya
k give me a sec let me think

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myininaya
  • myininaya
do you know trig substitution?
anonymous
  • anonymous
ya but was having trouble tring to find the right thing to plug in
myininaya
  • myininaya
=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
myininaya
  • myininaya
{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)
myininaya
  • myininaya
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)
myininaya
  • myininaya
is this helpful?
anonymous
  • anonymous
very helpful
myininaya
  • myininaya
should i go further? i havent done anything with the limits yet
anonymous
  • anonymous
na i can do the limits
myininaya
  • myininaya
k cool have fun
anonymous
  • anonymous
thx for the help
myininaya
  • myininaya
i had to complete the square above just so you know

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