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Hello everyone i'm studying for my calc 3 exam and I'm lost how they went from this substitution, my professor did the work.

Here is the problem and the answer under it:

http://img150.imageshack.us/img150/606/sssk5.jpg [Broken]

Well he showed the following:

1/2* integral 0 to PI/2; integral 0 to 1 u*cos(uv) dv du;

let t = uv;

then he got:

1/2 integral 0 to PI/2 u * 1/u sin(uv); now plug in 0 and 1 and he got:

1/2 * integral 0 to PI/2 sin(u) du = 1/2 cos(u) and plug in PI/2 and 0 and u get 1/2.

But what i'm lost on is, if you let t = uv;

then if you took the derivative of t, with respect to v you would get 0 wouldn't you? or do i take the partial deriviatve? if i took the partial derivative with respect to v, then i would get t = u; which would make sense i think...maybe not

Here is the problem and the answer under it:

http://img150.imageshack.us/img150/606/sssk5.jpg [Broken]

Well he showed the following:

1/2* integral 0 to PI/2; integral 0 to 1 u*cos(uv) dv du;

let t = uv;

then he got:

1/2 integral 0 to PI/2 u * 1/u sin(uv); now plug in 0 and 1 and he got:

1/2 * integral 0 to PI/2 sin(u) du = 1/2 cos(u) and plug in PI/2 and 0 and u get 1/2.

But what i'm lost on is, if you let t = uv;

then if you took the derivative of t, with respect to v you would get 0 wouldn't you? or do i take the partial deriviatve? if i took the partial derivative with respect to v, then i would get t = u; which would make sense i think...maybe not

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