3.a. Graph the equations y? = x – 2, y = x – 8. Shade in the region bounded by the three graphs.Label all important points on the graph (i.e. find the points of intersection).b. Set up the integral(s) that represent the area shaded in part a, with respect to x.C.Set up the integral(s) that represent the area shaded in part a, with respect to y.

Answered: a. Graph the equations y2 = x – 2, y =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

3.
a. Graph the equations y? = x – 2, y = x – 8. Shade in the region bounded by the three graphs.
Label all important points on the graph (i.e. find the points of intersection).
b. Set up the integral(s) that represent the area shaded in part a, with respect to x.
C.
Set up the integral(s) that represent the area shaded in part a, with respect to y.

Expert Solution

Step 1

a. Find the intersection point, as follows:

$\begin{array}{rcl} \sqrt{x - 2} & = & x - 8 \\ x - 2 & = & {(x - 8)}^{2} \\ x - 2 & = & x^{2} + 64 - 16 x \\ x^{2} - 17 x + 66 & = & 0 \\ x^{2} - 6 x - 11 x + 66 & = & 0 \\ x (x - 6) - 11 (x - 6) & = & 0 \\ (x - 6) (x - 11) & = & 0 \\ x & = & 6, 11 \\ y & = & x - 8 \\ = & 6 - 8 o r 11 - 8 \\ = & - 2 o r 3 \\ I n t e r s e c t i o n p o i n t s : \\ (6, - 2) a n d (11, 3) \end{array}$

Step 2

Graph and shade the bounded area, as follows:

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