Explain why or why not Determine whether the

QUESTION:

Explain why or why not  Determine whether the following statements are true and give an explanation or counterexample.

(a) It is possible that a computer algebra system says \(\int \frac{d x}{x(x-1)}=\ln (x-1)-\ln x\) and a table of integrals says \(\int \frac{d x}{x(x-1)}=\ln \left|\frac{x-1}{x}\right|+C\).

(b) A computer algebra system working in symbolic mode could give the result \(\int_{0}^{1} x^{8} d x=\frac{1}{9}\), and a computer algebra system working in approximate (numerical) mode could give the result \(\int_{0}^{1} x^{8} d x=0.11111111\).