## Line integral question, answer is here, just confused on it

Hello everyone i'm confused on this line integral.
The substiution is easy but i'm not sure where 2t is coming from...

integral over C x^2*y*sqrt(z) dz;
C: x = t^3;
y = t;
z = t^2;

0 <= t <= 1

integral over C x^2*y*sqrt(z) dz =
integral 0 to 1 (t^3)^2 (t) sqrt(t) * 2t dt =
integral 0 to 1 2*t^9 dt;

Okay I see they are just plugging in the t's for the x,y,z, but why do they write sqrt(t)? the sqrt(t^2) is just t.

Also where is this 2t dt coming from?

I thought maybe they used: sqrt(t^2); u = t^2;
du = 2t dt;
1/2*du = t dt;

Thanks
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 I guess sqrt(t) is just a typo. It should be sqrt(t^2) (Note that the final integral is t^9). And that 2tdt is equal to the differential dz.
 What Neutrino said. The final integrand should be 2t^9. In fact, if you compare step 2 to step 3, you'll find that it does not logically follow. So in all likelihood it was a typo.

## Line integral question, answer is here, just confused on it

THanks for the help guys!