   Chapter 8, Problem 4PS

Chapter
Section
Textbook Problem

Area Consider the problem of finding the area of the region bounded by the x-axis, the line x = 4 v, and the curve y = 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 pan (b).

To determine

To graph: The area of the region bounded by the curve y=x2(x2+9)32, x=0 and x=4.

Explanation

Given:

The function provided is:

y=x2(x2+9)32

Graph:

For the function y=x2(x2+9)32 the graph is drawn as below:

Use Ti-83 to plot the graph of the function:

Step 1: Press the [Y=]key, then there will appear the equations for y.

Step 2: Enter the equations in Y1. Here, Y1=x2(x2+9)32

(b)

To determine

To calculate: Thevalue of area of y=x2(x2+9)32 by trigonometric substitution

(c)

To determine

To calculate: By trigonometric substitution the value of area of y=x2(x2+9)32 of x=3sinhu

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