Consider the integral I = fa x arctan(x) dx. (a) Write explicitly an approximation for I using the right-hand sum with n-slices. You can use the sigma notation or the notation. *** (b) Find a number of slices for which your approximation in part (a) is smaller than 10-6. Hint: the error bound formula for the right-hand sum is |I – Rn| < M(1) (b-a) ² where M(1) is an upper bound for f'(x) on [a, b]. 2n "
Consider the integral I = fa x arctan(x) dx. (a) Write explicitly an approximation for I using the right-hand sum with n-slices. You can use the sigma notation or the notation. *** (b) Find a number of slices for which your approximation in part (a) is smaller than 10-6. Hint: the error bound formula for the right-hand sum is |I – Rn| < M(1) (b-a) ² where M(1) is an upper bound for f'(x) on [a, b]. 2n "
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider the integral I = fx arctan(x)dx.
(a) Write explicitly an approximation for I using the right-hand sum with n-slices. You can use the
sigma notation or the ... notation.
(b) Find a number of slices for which your approximation in part (a) is smaller than 10-6. Hint:
the error bound formula for the right-hand sum is I – Rn| < M(1) (b-a)²
where M(1) is an upper
bound for f'(x)| on [a, b].
2n
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c62f25d-777b-43ca-b863-a138e4dcafb3%2F7aeef590-8e88-42f7-9214-f6a99b9570f0%2Fvinsri_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the integral I = fx arctan(x)dx.
(a) Write explicitly an approximation for I using the right-hand sum with n-slices. You can use the
sigma notation or the ... notation.
(b) Find a number of slices for which your approximation in part (a) is smaller than 10-6. Hint:
the error bound formula for the right-hand sum is I – Rn| < M(1) (b-a)²
where M(1) is an upper
bound for f'(x)| on [a, b].
2n
2
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