Chapter 8, Problem 4PS

Area Consider the problem of finding the area of the region bounded by the x-axis, the line $x=4$, and the curve

$y=\frac{x^2}{{(x^2+9)}^{3/2}}$.

(a) Use a graphing utility to graph the region and approximate its area.

(b) Use an appropriate trigonometric substitution to find the exact area.

(c) Use the substitution $x=3\sinh u$ to find the exact area and verify that you obtain the same answer as in part (b).