Consider the definite integral •1 1 1 - 1/₁² 1 ² x dx = 1+x 0 a) Use an approximation scheme with n = 2 subintervals of equal width to approximate the definite integral above. Round your answer to two decimal places. b) If ||f"(x)|| ≤ K for a ≤ x ≤ b and use this to find the error bound. And determine how large n must be to guarantee that the approximation using your approximation scheme with n subintervals has an error less that 0.00001.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Problem (5)
Consider the definite integral
I
1
1
= √₁²₁ ₁² ² + x ² x
dx
1+x
a) Use an approximation scheme with n= 2 subintervals of equal
width to approximate the definite integral above. Round your
answer to two decimal places.
b) If ||f"(x)|| ≤ K for a ≤ x ≤ b and use this to find the error
bound. And determine how large n must be to guarantee that
the approximation using your approximation scheme with n
subintervals has an error less that 0.00001.
Transcribed Image Text:Problem (5) Consider the definite integral I 1 1 = √₁²₁ ₁² ² + x ² x dx 1+x a) Use an approximation scheme with n= 2 subintervals of equal width to approximate the definite integral above. Round your answer to two decimal places. b) If ||f"(x)|| ≤ K for a ≤ x ≤ b and use this to find the error bound. And determine how large n must be to guarantee that the approximation using your approximation scheme with n subintervals has an error less that 0.00001.
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