Chapter 8.4, Problem 42E

a.

To determine

Compute the area under the graph of $y=\tanh x\text{ for }0\le x\le 4$

b.

To determine

Compute the area under the graph of $y={\tanh }^{-1}x\text{ for }0\le x\le \tanh 4$

c.

To determine

Show that the sum of the areas in (a) and (b) is equal to $4\tanh 4$

d.

To determine

Explain why the sum of the areas in (a) and (b) is equal to $4\tanh 4$