anonymous
  • anonymous
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Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
midhun.madhu1987
  • midhun.madhu1987
?
anonymous
  • anonymous
|dw:1437384213608:dw|
anonymous
  • anonymous
I have tried diffrent approaches but end up with the same result that doesnt match the correct answer.

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More answers

amoodarya
  • amoodarya
\[t^2-3=u\\t=3 \rightarrow 9-3=u \rightarrow u=6\\t=4\rightarrow 16-3=u \rightarrow u=13\\t^2-3=u \rightarrow 2tdt=du \\\frac{tdt}{\sqrt{t^2-3}}=\frac{1}{2} \frac{du}{\sqrt{u}}\]
UsukiDoll
  • UsukiDoll
u subsitution like what @amoodarya did
anonymous
  • anonymous
|dw:1437384771141:dw|
UsukiDoll
  • UsukiDoll
and then take the antiderivative after u = ... du = dx steps
amoodarya
  • amoodarya
or see this \[\frac{t}{\sqrt{t^2-3}}=\frac{2t}{2\sqrt{t^2-3}}=\frac{(t^-3)'}{2\sqrt{t^2-3}}\\=\frac{d}{dt}\sqrt{t^2-3}\\ \int\limits_{3}^{4}\frac{d}{dt}\sqrt{t^2-3} =\sqrt{t^2-3}|_{3,4}=\sqrt{3^2-3}-\sqrt{4^2-3}\]
UsukiDoll
  • UsukiDoll
then plug u back in and evaluate f(4)-f(3)
anonymous
  • anonymous
why doesnt mine work?
UsukiDoll
  • UsukiDoll
|dw:1437385040459:dw| find the derivative of u
anonymous
  • anonymous
2t and then?
anonymous
  • anonymous
ohhhh Now I get it...
UsukiDoll
  • UsukiDoll
|dw:1437385150396:dw| so we just need to divide 2 on both sides
UsukiDoll
  • UsukiDoll
then that tdt should be 1/2
UsukiDoll
  • UsukiDoll
|dw:1437385229449:dw|
UsukiDoll
  • UsukiDoll
|dw:1437385312000:dw|
UsukiDoll
  • UsukiDoll
|dw:1437385348540:dw|
UsukiDoll
  • UsukiDoll
|dw:1437385408712:dw|
UsukiDoll
  • UsukiDoll
now sub u back u = t^2 -3 |dw:1437385433088:dw|
UsukiDoll
  • UsukiDoll
|dw:1437385518425:dw|
UsukiDoll
  • UsukiDoll
|dw:1437385586233:dw| you should be getting this after evaluation
anonymous
  • anonymous
Yeah, this was way easier. THanks!
UsukiDoll
  • UsukiDoll
I was double checking with wolfram we got the right answer, but they took it a step further by multiplying 4 throughout the answer |dw:1437385928137:dw|
UsukiDoll
  • UsukiDoll
wouldn't matter...it's the same thing :P
anonymous
  • anonymous
Appreciate ur time and patience. Thank you:)
UsukiDoll
  • UsukiDoll
you're welcome :)

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