Determine the centroid of the area shown when a = 5 in. a y Y X Qx = SZ Integral Table: Includes MATLAB commands after >>syms x y x1 x2; >> f=1/x^2; Area = √²dx = -1/2 = int( f, x, x1,x2) = int( int(1,y,0,f), x, x1, x2) de Z1 Qy= ²² x ½ dx = ln(x2) – ln(x1) · I 1/2² 2 y= 22/2/2/2 da a in. in. X In(x₁) = int( x* f, x, x1,x2) = int( int(x,y,0,f), x, x1, x2) = 6 (21)²6 (22)² = int( (f/2) * f, x, x1,x2) = int( int(y.y,0,f), x, x1, x2)
Determine the centroid of the area shown when a = 5 in. a y Y X Qx = SZ Integral Table: Includes MATLAB commands after >>syms x y x1 x2; >> f=1/x^2; Area = √²dx = -1/2 = int( f, x, x1,x2) = int( int(1,y,0,f), x, x1, x2) de Z1 Qy= ²² x ½ dx = ln(x2) – ln(x1) · I 1/2² 2 y= 22/2/2/2 da a in. in. X In(x₁) = int( x* f, x, x1,x2) = int( int(x,y,0,f), x, x1, x2) = 6 (21)²6 (22)² = int( (f/2) * f, x, x1,x2) = int( int(y.y,0,f), x, x1, x2)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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2.
![**Determine the Centroid of the Area when \( a = 5 \, \text{in.} \)**
**Diagram Description:**
The diagram shows a shaded area under the curve \( y = \frac{1}{x^2} \), bounded by the x-axis and vertical lines at \( x = 1 \) and \( x = a \). The width and height of the shaded region are both labeled as \( a \).
**Integral Table: MATLAB Commands and Calculations**
1. **Area Calculation:**
\[
\text{Area} = \int_{x_1}^{x_2} \frac{1}{x^2} \, dx = -\frac{1}{x_2} + \frac{1}{x_1}
\]
MATLAB commands:
```matlab
syms x y x1 x2
f = 1/x^2;
Area = int(f, x, x1, x2) = int(int(1, y, 0, f), x, x1, x2)
```
2. **\( Q_y \) Calculation:**
\[
Q_y = \int_{x_1}^{x_2} \frac{1}{x^2} \, dx = \ln(x_2) - \ln(x_1)
\]
MATLAB commands:
```matlab
Qy = int(x*f, x, x1, x2) = int(int(x*y, 0, f), x, x1, x2)
```
3. **\( Q_x \) Calculation:**
\[
Q_x = \int_{x_1}^{x_2} \frac{1}{2} \cdot \frac{1}{x^2} \, dx = \frac{1}{6(x_1)^3} - \frac{1}{6(x_2)^3}
\]
MATLAB commands:
```matlab
Qx = int((f/2)*f, x, x1, x2) = int(int(y*y, 0, f), x, x1, x2)
```
**Centroid Coordinates:**
\[
\bar{Y} : \, \_\_\_\_ \, \text{in.}
\]
\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51e7283f-1187-4641-a7dd-756ddc41b628%2F7c862d36-c0ea-4d1f-b36f-6f9d5cd00e39%2Fo972dy_processed.png&w=3840&q=75)
Transcribed Image Text:**Determine the Centroid of the Area when \( a = 5 \, \text{in.} \)**
**Diagram Description:**
The diagram shows a shaded area under the curve \( y = \frac{1}{x^2} \), bounded by the x-axis and vertical lines at \( x = 1 \) and \( x = a \). The width and height of the shaded region are both labeled as \( a \).
**Integral Table: MATLAB Commands and Calculations**
1. **Area Calculation:**
\[
\text{Area} = \int_{x_1}^{x_2} \frac{1}{x^2} \, dx = -\frac{1}{x_2} + \frac{1}{x_1}
\]
MATLAB commands:
```matlab
syms x y x1 x2
f = 1/x^2;
Area = int(f, x, x1, x2) = int(int(1, y, 0, f), x, x1, x2)
```
2. **\( Q_y \) Calculation:**
\[
Q_y = \int_{x_1}^{x_2} \frac{1}{x^2} \, dx = \ln(x_2) - \ln(x_1)
\]
MATLAB commands:
```matlab
Qy = int(x*f, x, x1, x2) = int(int(x*y, 0, f), x, x1, x2)
```
3. **\( Q_x \) Calculation:**
\[
Q_x = \int_{x_1}^{x_2} \frac{1}{2} \cdot \frac{1}{x^2} \, dx = \frac{1}{6(x_1)^3} - \frac{1}{6(x_2)^3}
\]
MATLAB commands:
```matlab
Qx = int((f/2)*f, x, x1, x2) = int(int(y*y, 0, f), x, x1, x2)
```
**Centroid Coordinates:**
\[
\bar{Y} : \, \_\_\_\_ \, \text{in.}
\]
\
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