- #1
mr_coffee
- 1,629
- 1
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
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