n 6. (a) Use induction to prove the summation formula ²: x² dx. i=1 (b) Show that the function x → x² is Riemann integrable on the interval [0, 1] and compute 1² 2² Hint: Use the sequential criterion, where Pn E n(n + 1)(2n + 1) 6 = {0, 1/2 , /1/2 › n'n' ,1}.
n 6. (a) Use induction to prove the summation formula ²: x² dx. i=1 (b) Show that the function x → x² is Riemann integrable on the interval [0, 1] and compute 1² 2² Hint: Use the sequential criterion, where Pn E n(n + 1)(2n + 1) 6 = {0, 1/2 , /1/2 › n'n' ,1}.
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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![n
x² dx.
n(n + 1)(2n + 1)
6
6. (a) Use induction to prove the summation formula
i=1
(b) Show that the function x → x² is Riemann integrable on the interval [0, 1] and compute
1
[2²
Hint: Use the sequential criterion, where Pn
{0, 1/2, 2/12,..., 1}.
n'](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e52190b-50e6-4255-84a6-de0c6d0112f2%2F411c59cf-19e6-431b-bee9-2d9ab2c2213d%2Fp86uyvj_processed.png&w=3840&q=75)
Transcribed Image Text:n
x² dx.
n(n + 1)(2n + 1)
6
6. (a) Use induction to prove the summation formula
i=1
(b) Show that the function x → x² is Riemann integrable on the interval [0, 1] and compute
1
[2²
Hint: Use the sequential criterion, where Pn
{0, 1/2, 2/12,..., 1}.
n'
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