(a) Compute the area under the graph of y = tanh x for 0 ≤ x ≤ 4.
(b) Compute the area under the graph of y = tanh⁻¹ x for 0 ≤ x ≤ tanh 4.
(c) Show that the sum of the areas in (a) and (b) is equal to 4 tanh 4.
(d) Similar to Exercise 41(d), explain graphically why the sum of the areas in (a) and (b) is equal to 4 tanh 4.

Data From Exercise 41(d)

(d) Refer to Figure 1 and explain why the sum of the areas in (a) and (b) is equal to 5 sinh 5.

sinh 5 y = sinh x 5 X