Chapter 5.6, Problem 53ES

A student wants to find the area enclosed by the graphs of $y=1/\sqrt{1-x^2},y=0,x=0,$ and $x=0.8$ .

(a) Show that the exact area is ${\sin }^{-1}0.8$ .

(b) The student uses a calculator to approximate the result in part (a) to two decimal places and obtains an incorrect answer of $53.13$ . What was the student’s error? Find the correct approximation.