Calculate the integral approximations T6 and Me for (In x)-¹dx. Your answers must be accurate to 8 decimal places. T6 2.7898007 = M6= 2.750596917
Calculate the integral approximations T6 and Me for (In x)-¹dx. Your answers must be accurate to 8 decimal places. T6 2.7898007 = M6= 2.750596917
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Calculating Integral Approximations Using Trapezoidal and Midpoint Rules**
In this exercise, we are tasked with calculating the integral approximations \( T_6 \) and \( M_6 \) for the integral
\[
\int_{4}^{9} (\ln x)^{-1} \, dx.
\]
Your answers must be accurate to 8 decimal places.
**Results:**
- The approximation using the Trapezoidal rule with 6 subintervals (\( T_6 \)):
\[
T_6 = 2.7898007
\]
(This result is displayed with a pink background.)
- The approximation using the Midpoint rule with 6 subintervals (\( M_6 \)):
\[
M_6 = 2.750596917
\]
(This result is displayed with a green background.)
These results show the computed values of the integral using two different numerical integration methods, providing insights into approximation accuracy to 8 decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85a13651-0641-4e1f-9366-64e873b85445%2F5e739f66-6a8f-417e-976b-f82e8f21a3d2%2Fftaprsm_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculating Integral Approximations Using Trapezoidal and Midpoint Rules**
In this exercise, we are tasked with calculating the integral approximations \( T_6 \) and \( M_6 \) for the integral
\[
\int_{4}^{9} (\ln x)^{-1} \, dx.
\]
Your answers must be accurate to 8 decimal places.
**Results:**
- The approximation using the Trapezoidal rule with 6 subintervals (\( T_6 \)):
\[
T_6 = 2.7898007
\]
(This result is displayed with a pink background.)
- The approximation using the Midpoint rule with 6 subintervals (\( M_6 \)):
\[
M_6 = 2.750596917
\]
(This result is displayed with a green background.)
These results show the computed values of the integral using two different numerical integration methods, providing insights into approximation accuracy to 8 decimal places.
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