Chapter 7.4, Problem 42E

To determine

(a)

To compute:

The area under the graph of $y=\tanh x$ for $0\le x\le 4$.

To determine

(b)

To compute:

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

To determine

(c)

To show:

The sum of area of part a and part b is $4\tanh 4$.

To determine

(d)

To explain:

The sum of area in (a) and (b) is equal to $5\sinh 5$.