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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