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Question : 75 of 160
Marks:
+1,
-0
Solution:
From the given expression,
A6=e−xcos6xdx =[−e−xcos6x]∞−(−e−x) 6cos5x(−sin‌x)dx =0−6‌e−xcos5x‌sin‌x‌d‌x This gives,
=e−xcos5x‌sin‌x‌d‌x A6=([−e−xcos5x‌sin‌x‌ ]∞ −(−e−x)[5cos4x(−sin‌x)‌sin‌x+cos5x.cos‌x]dx) =0+(e−x)[−5cos4x(1−cos2x ) +cos6x]‌d‌x =−5‌(e−x)[cos4x]dx+6‌(e−x )[cos6x]dx This implies,
−A6=−5A4+6A6 5A4=A6 A6=A4 Now,
= =
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