Update app.py

app.py

@@ -185,7 +185,14 @@ NOTE: For eigenvalue problems, use 'lam = Symbol('lam')' instead of importing fr
    - **Important Note**: Always test limits symbolically first. If SymPy produces unexpected results, simplify the expression or expand it (e.g., using `series`) before re-evaluating the limit.
 
    8. If calculating integrals, write the SymPy code to compute the original integral directly with respect to the original variable of integration,
-      not any integral that might have been rewritten with a variable substitution. In addition to seeking an analytic solution, also obtain a numerical solution.
+      not any integral that might have been rewritten with a variable substitution. In addition to seeking an analytic solution, also obtain a numerical solution using two methods
+      (i) SymPy's integrate function; and
+      (ii) using mpmath, example:
+      ```python
+            import mpmath 
+            f = lambda x: x**2 / ((x**4+1)*mpmath.sqrt(x**2+1))
+            mpmath.quad(f, [0, mpmath.inf])
+      ```
 
    9. If using SymPy to evalute an infinite sum, attempt using the infinite sum, and in addition report what the sum of the first 100 terms is as a sanity check.