Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16 exact value of the integral is given for computing the error. 5 $(x²- 1 Complete the following table. (Type integers or decimals.) M(n) 222 n (6x²-2x) dx = 224 4 8 T(n) 228 Absolute Error in M(n) 2 ... Absolute Error in T(n) 4
Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16 exact value of the integral is given for computing the error. 5 $(x²- 1 Complete the following table. (Type integers or decimals.) M(n) 222 n (6x²-2x) dx = 224 4 8 T(n) 228 Absolute Error in M(n) 2 ... Absolute Error in T(n) 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please help with table for n=8, n=16, n=32
![**Applying Midpoint and Trapezoid Rules**
We apply the Midpoint and Trapezoid Rules to the following integral:
\[
\int_{1}^{5} (6x^2 - 2x) \, dx = 224
\]
Create a table showing the approximations and errors for \( n = 4, 8, 16, \) and \( 32 \). The exact value of the integral is provided for computing the error.
**Table:**
| \( n \) | \( M(n) \) | \( T(n) \) | Absolute Error in \( M(n) \) | Absolute Error in \( T(n) \) |
|---------|-----------|------------|-------------------------------|-------------------------------|
| 4 | 222 | 228 | 2 | 4 |
| 8 | | | | |
- **\( n \)**: The number of subdivisions.
- **\( M(n) \)**: Approximation using the Midpoint Rule.
- **\( T(n) \)**: Approximation using the Trapezoid Rule.
- **Absolute Error**: The absolute difference between the approximation and the exact value 224.
Continue filling the table for \( n = 8, 16, \) and \( 32 \). Calculate the approximations and the corresponding errors for each method.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa204fb01-1593-427c-b210-f132b42420bd%2Ffb5385e7-08b7-44ef-90a1-64790fdb776d%2Flf8zcl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Applying Midpoint and Trapezoid Rules**
We apply the Midpoint and Trapezoid Rules to the following integral:
\[
\int_{1}^{5} (6x^2 - 2x) \, dx = 224
\]
Create a table showing the approximations and errors for \( n = 4, 8, 16, \) and \( 32 \). The exact value of the integral is provided for computing the error.
**Table:**
| \( n \) | \( M(n) \) | \( T(n) \) | Absolute Error in \( M(n) \) | Absolute Error in \( T(n) \) |
|---------|-----------|------------|-------------------------------|-------------------------------|
| 4 | 222 | 228 | 2 | 4 |
| 8 | | | | |
- **\( n \)**: The number of subdivisions.
- **\( M(n) \)**: Approximation using the Midpoint Rule.
- **\( T(n) \)**: Approximation using the Trapezoid Rule.
- **Absolute Error**: The absolute difference between the approximation and the exact value 224.
Continue filling the table for \( n = 8, 16, \) and \( 32 \). Calculate the approximations and the corresponding errors for each method.
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