anonymous
  • anonymous
evaluate s x( (8+2x-x^2) )^1/2 dx p/s: s is for integrate
Mathematics
schrodinger
  • schrodinger
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Mimi_x3
  • Mimi_x3
I assume its an integral \[\int\limits x\sqrt{8+2x-x^{2}}dx \] Well, complete the square first; then looks like a sub
anonymous
  • anonymous
yes. I've done the completing the square but not sure whats the next step. by part or substitution?
Mimi_x3
  • Mimi_x3
looks like a substitution would be easier

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anonymous
  • anonymous
ok. i"ll try again. tq :)
anonymous
  • anonymous
still dont get it. help me plez :(
Mimi_x3
  • Mimi_x3
\[\int\limits x\sqrt{-x^{2}+2x+8} dx => \int\limits x\sqrt{-(x^{2}-2x-8)} dx => \int\limits x\sqrt{-((x^{2}-1)^{2}-(1)^{2}+8))} dx\] \[=> \int\limits x\sqrt{-(x^{2}-1)-9} dx => \int\limits x\sqrt{9-(x-1)^{2}} dx\] let u = x-1 -> x = u+1 \[=> \int\limits\left(u+1\right)\sqrt{9-u^{2}}du \]
Mimi_x3
  • Mimi_x3
then it's trig sub
Mimi_x3
  • Mimi_x3
\[ x= sin\theta\]
anonymous
  • anonymous
ok mimi.i'll try. thanks again.
Mimi_x3
  • Mimi_x3
np and for this u = 3sin\theta

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