Q. 31 In Exercises 31鈥�34, use a weig... [FREE SOLUTION]

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Chapter 6: Q. 31 (page 556)

In Exercises 31鈥�34, use a weighted average over n rectangles to approximate the centroid of the region described.
The region between f(x) = 鈭歺 and the x-axis on [a, b] = [1, 9], with n = 2.

Short Answer

Expert verified

$C e n t r e o f m a s s : (- 0.37, 1.22)$

Step by step solution

Step1. Given Information

region,

$f (x) = \sqrt{x}$

Step2. Calculate

$A = {鈭�}_{- 1.31}^{0.54} 2 - x^{2} - e^{x} d x A = 2 x - \frac{x^{3}}{3} - e^{x} {|_{- 1.31}}^{0.54} A = 1.45$

Step3. Continue

$\overset{炉}{x} = \frac{1}{A} {鈭�}_{a}^{b} x f (x) 蚁 (x) d x 鈬� \overset{炉}{x} = \frac{1}{1.45} {鈭�}_{- 1.31}^{0.54} (2 x - x^{3} - x e^{x}) d x \overset{炉}{x} = \frac{1}{1.45} [x^{2} - \frac{x^{4}}{4} - (x e^{x} - e^{x}) {|_{- 1.31}}^{0.54}] = - 0.3711 \overset{炉}{y} = \frac{1}{A} {鈭�}_{a}^{b} (f^{2} (x) - 蚁^{2} (x)) d x 鈬� \frac{1}{1.45} {鈭�}_{- 1.31}^{0.54} (\frac{1}{2}) [{(2 - x)}^{2} - e^{2 x}] d x \overset{炉}{y} = 0.345 {鈭�}_{- 1.31}^{0.54} 4 - 4 x^{2} + x^{4} - e^{2 x} d x \overset{炉}{y} = 0.345 [4 x - \frac{4 x^{3}}{3} + \frac{x^{5}}{5} - \frac{e^{2 x}}{2} {|_{- 1.31}}^{0.54}] \overset{炉}{y} = 1.22 C . o . M : (- 0.37, 1.22) .$

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91影视

In Exercises 31鈥�34, use a weighted average over n rectangles to approximate the centroid of the region described.
The region between f(x) = 鈭歺 and the x-axis on [a, b] = [1, 9], with n = 2.

Short Answer

Step by step solution

Step1. Given Information

Step2. Calculate

Step3. Continue

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91影视

In Exercises 31鈥�34, use a weighted average over n rectangles to approximate the centroid of the region described.The region between f(x) = 鈭歺 and the x-axis on [a, b] = [1, 9], with n = 2.

Short Answer

Step by step solution

Step1. Given Information

Step2. Calculate

Step3. Continue

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Decision Maths

Pure Maths

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

In Exercises 31鈥�34, use a weighted average over n rectangles to approximate the centroid of the region described.
The region between f(x) = 鈭歺 and the x-axis on [a, b] = [1, 9], with n = 2.