Answer: Graphical Reasoning Consider the region bounded by the graphs of and where (a)

Chapter 7, Problem 51

(choose chapter or problem)

Graphical Reasoning Consider the region bounded by the graphs of \(y=x^{2}\) and y = b, where b > 0.

(a) Sketch a graph of the region.

(b) Use the graph in part (a) to determine \(\bar{x}\). Explain.

(c) Set up the integral for finding \(M_{y}\). Because of the form of the integrand, the value of the integral can be obtained without integrating. What is the form of the integrand ? What is the value of the integral? Compare with the result in part (b).

(d) Use the graph in part (a) to determine whether \(\bar{y}>\frac{b}{2}\) or \(\bar{y}<\frac{b}{2}\). Explain.

(e) Use integration to verify your answer in part (d).

Text Transcription:

y=x^2

bar x

M_y

bar y>b/2

bar y<b/2