Integrate? t2tdt

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Answer 1 · 2018-03-01T12:58:29

Let, #dx=t 2t dt#

so, #dx = 2t^2 dt#

or, #int dx = 2 int t^2 dt#

or, #x = 2/3 t^3 +c#

Answer 2 · 2018-03-01T13:18:47

#(2t^3)/3+C#

Given: #intt2tdt#

#=int2t^2dt#

We can use the constant rule here, which states if #a# is constant, then #intaf(x)dx=aintf(x)dx#.

We can apply the rule here, and get

#=2intt^2dt#

Using the power rule, #inta^ndx=(a^(n+1))/(n+1), n!=1#. So here, we get

#=2t^3/3+C#

#=(2t^3)/3+C#