272 Sketch sin for n = 1 and n = 2 over the intervals 0 to a andand. Using even and odd arguments, explain why the following integrals are zero: and that 5 (₁7²) and cos sin (¹²) cos (²) a Jo sin (1) cos a nπx a 0 = 0 Using the fact that sin 2x = 2 sin x cos x prove that the above integrals are zero.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
nπx
a
and that
12. Sketch sin
0 to a andand. Using even and odd arguments, explain why the
following integrals are zero:
and cos nTx for n = 1 and n = 2 over the intervals
a
L²sin (¹²) cos (¹²) =
= 0
a
a
"* sin (na) cos (1²)
a
= 0
13. Using the fact that sin 2x = 2 sin x cos x prove that the above integrals
are zero.
Transcribed Image Text:nπx a and that 12. Sketch sin 0 to a andand. Using even and odd arguments, explain why the following integrals are zero: and cos nTx for n = 1 and n = 2 over the intervals a L²sin (¹²) cos (¹²) = = 0 a a "* sin (na) cos (1²) a = 0 13. Using the fact that sin 2x = 2 sin x cos x prove that the above integrals are zero.
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