(b) Defined f(x) = > an sin nx = a1 sin x + a2 sin 2x + .. .aN sin Nr, %3D n=1 where N is a positive integer and a1, a2, ....., ayas a constant. Use part (a) to show that 1 am sin mx dx | for m=1, 2,.,N . [Hint: Use integral linear property]
(b) Defined f(x) = > an sin nx = a1 sin x + a2 sin 2x + .. .aN sin Nr, %3D n=1 where N is a positive integer and a1, a2, ....., ayas a constant. Use part (a) to show that 1 am sin mx dx | for m=1, 2,.,N . [Hint: Use integral linear property]
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
DO PART B ONLY!
THANKS IN ADVANCE
![(a) Let m and n be positive integers. Show that
if
m = n,
sin mx sin nx dx =
0 if
m + n.
(b) Defined
N
f (x) = > an sin na a1 sin x + a2 sin 2x +...aN sin Na,
%3D
n=1
where N is a positive integer and a,, a2, ...., ayas a constant. Use part (a) to show that
f(x)
ат
sin mx
dx
-
T
for m=1, 2,.,N . [Hint: Use integral linear property]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4790574a-44e3-4391-ba92-aebffa7965a4%2F275170a7-b2ed-4418-ba18-2ff850b5de78%2Fqgkrcrq_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Let m and n be positive integers. Show that
if
m = n,
sin mx sin nx dx =
0 if
m + n.
(b) Defined
N
f (x) = > an sin na a1 sin x + a2 sin 2x +...aN sin Na,
%3D
n=1
where N is a positive integer and a,, a2, ...., ayas a constant. Use part (a) to show that
f(x)
ат
sin mx
dx
-
T
for m=1, 2,.,N . [Hint: Use integral linear property]
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