KatClaire
Find the following integral
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kugler97
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what is the integer?
KatClaire
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\[\int\limits_{}^{} \frac{ (2t+1)^{2} }{ \sqrt{t} } dt\]
KatClaire
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does \[\frac{ t ^{2} }{ \sqrt{t} } \] cancel out????
RadEn
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u need to expand of (2t + 1)^2 = 4t^2 + 4t + 1
and convert sqrt(t) = t^(1/2)
now, can u simplify (4t^2 + 4t + 1)/t^(1/2) ?
kugler97
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yea i think it does lol
KatClaire
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well I'll show you how far I got \[4 \int\limits_{}^{} \frac{ t ^{2} }{ t ^{1/2} } +4 \int\limits_{}^{} \frac{ t }{ t ^{1/2} } + \int\limits_{}^{} \frac{ 1 }{ t ^{1/2} }\]
RadEn
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so far is good, then use the properties of exponent to simplify of them :
|dw:1358987039172:dw|
RadEn
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now, what would be ur integral ?
KatClaire
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Sorry openstudy crapped out last night lol thanks
RadEn
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nopes.. :)
btw, do u got it ?
KatClaire
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Mhmm :) I got
\[\frac{ 8t ^{^{5/2}} }{ 5 }+\frac{ 8t ^{3/2} }{ 3 }+ 2t ^{1/2}+c\]
Look about right?
RadEn
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yeah, i have cheked ur answer
you are right :)
KatClaire
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Hehe you are the best thanks!!!!
RadEn
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you're welcome