anonymous
  • anonymous
Find the indicated integral using the method of substitution. 3t[(t^2+8)^1/2] dt
Mathematics
katieb
  • katieb
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amistre64
  • amistre64
trig substitution? or otherwise?
anonymous
  • anonymous
i think he means regular sub
anonymous
  • anonymous
there's no need for a trig id here

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amistre64
  • amistre64
but, but..... i wanna do a trig ;)
anonymous
  • anonymous
rofllls, do the one from this afternoon!
amistre64
  • amistre64
lol :)
amistre64
  • amistre64
3t sqrt(t^2 +8); u = t^2 + 8; du = 2t dx; dx = du/2t
amistre64
  • amistre64
3t sqrt(u) du ---------- = (3/2) sqrt(u) du 2t
anonymous
  • anonymous
3t[(t^2+8)^1/2] dt u = t^2 + 8 du = 2t dt \[\frac{3}{2}\int\limits_{}^{}u^{\frac{1}{2}}du = \frac{3}{2}*\frac{2}{3} u ^{\frac{3}{2}} = (t^2 + 8)^{\frac{3}{2}}\]
amistre64
  • amistre64
(3/2) [S] u^(1/2) du (3/2) (2/3) u^(3/2) = u^(3/2)
anonymous
  • anonymous
i win :P
amistre64
  • amistre64
yes you do :) and i added a dx for some reason ;)
anonymous
  • anonymous
it's just variables...i'm used to dx also =/ i hate the fact that they switch up variables...
anonymous
  • anonymous
Thanks!

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