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3. Verify the result shown using 'integration by parts'. | t sin(nt) dt = – -t 1 t cos(nt) + 1 sin(nt) %3D n n2

3. Verify the result shown using 'integration by parts'. | t sin(nt) dt = – -t 1 t cos(nt) + 1 sin(nt) %3D n n2

Advanced Engineering Mathematics
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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Let f(x) be a function of variable x defined on an interval 0 to T. It can be represented by the Fourier series, given by {(2) = +Ean 2nn (2nt +> an cos T *) + b, sin T where (2nn 2na f(u)du, an ( (u) cos (u) du, b. = -и) du, bn T I f(u) sin ao = -u) du. Answer the following questions. 3. Verify the result shown using 'integration by parts'. 1 1 | t sin(nt) dt = -- t cos(nt) + sin(nt) n2 n
Transcribed Image Text:Let f(x) be a function of variable x defined on an interval 0 to T. It can be represented by the Fourier series, given by {(2) = +Ean 2nn (2nt +> an cos T *) + b, sin T where (2nn 2na f(u)du, an ( (u) cos (u) du, b. = -и) du, bn T I f(u) sin ao = -u) du. Answer the following questions. 3. Verify the result shown using 'integration by parts'. 1 1 | t sin(nt) dt = -- t cos(nt) + sin(nt) n2 n
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