(25) Let k and n be positive integers. Prove each of the following: sin (n2) dz = | cos (nx) dz = 7. b) | sin(kr) cos(nr) dr = 0. e) L. sin(kr) sin(nr) dr = | cos(ma) cos(nr) dr = 0 if m + n.
(25) Let k and n be positive integers. Prove each of the following: sin (n2) dz = | cos (nx) dz = 7. b) | sin(kr) cos(nr) dr = 0. e) L. sin(kr) sin(nr) dr = | cos(ma) cos(nr) dr = 0 if m + n.
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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Question
Let k and n be positive integers. Prove each of the following:
a) π
−π
sin2(nx) dx =
π
−π
cos2(nx) dx = π.
b) π
−π
sin(kx) cos(nx) dx = 0.
c) π
−π
sin(kx) sin(nx) dx =
π
−π
cos(mx) cos(nx) dx = 0 if
m = n.
Transcribed Image Text:(25) Let k and n be positive integers. Prove each of the following:
a)
sin* (n.x) dz = |
cos (nx) dz = 7.
b)
sin(kr) cos(nr) dr = 0.
%3D
c)
sin(kr) sin(nz) dr =
/ cos(ma) cos(na) dr = 0 if
m + n.
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