Symbolic solve
Following the change of variable thread, I wanted to streamline the whole process.
Namely, using the same example in the above thread, I'd like to say
integral_def_change(x*cos(x^2+1), (x, 0, 2*pi), u == x^2 + 1, u)
The difference is, I wanted also Sage to automatically solve for x
instead of providing x = sqrt(u - 1)
, say. But when I tried
solve(u == x^2 + 1, x)[0].rhs()
the output was r1
.
1- What exactly is r1 ??
A way out (see this thread)
seems to make of the solution a function of u
f(u) = solve(u == x^2 + 1, x)[0].rhs()
Now f is
u |--> -sqrt(u - 1)
2- What can I do to get +sqrt(u - 1)
instead? Is this related to the
positive function question there?