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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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|dw:1437384213608:dw|
I have tried diffrent approaches but end up with the same result that doesnt match the correct answer.

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

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