Hello: Is there a way Mathematica to transform a definite integral in t into a function in x, per the FTC1 equation:
g[x_] = (
\*SubsuperscriptBox[\(\[Integral]\), \(2\), \(x\)]\(
\*FractionBox[\(
\*SuperscriptBox[\(t\), \(2\)] - 1\), \(
\*SuperscriptBox[\(t\), \(2\)] + 1\)] \[DifferentialD]t\)\)
The software just spins when I try this, either as '=' or ':='. I've also tried both:
g[x] = Integrate[f[t], {t, 2, x}]
g[x] = Integrate[f[t], {x, 2, x}]
The first just spins. The second returns:
((-1 + t^2) (-2 + x))/(1 + t^2)
...which is interesting, but not the function completely in x I was looking for.
I guess another way of putting my question is, can we get M. to handle upper and/or lower limits of integration as variables?
Thanks, TB
Integrate[(t^2 - 1)/(t^2 + 1), {t, 2, x}, GenerateConditions -> False]
? $\endgroup$g[x_] = Integrate[f'[t], {t, 2, x}]
yields-f[2] + f[x]
$\endgroup$