∞
In = ∫ e-x(sin x)n dx (n>1), then value of 101 I10I8
o is equal to....................
ANS [ 90 ]
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1 Answers
29Manamy...actually Latex is not working..so i am unable to post the solution..btw i can tell u the method how to solve this question..
break ∫e-x(sinx)n = ∫e-x(sinx)n-1 * sinx
= e-x(sinx)n-1 ∫ sinxdx - ∫[e-x(sinx)n-2 (n-1)cosx - e-x(sinx)n-1]cosx
= -e-x(sinx)n-1cosx - ∫[e-x(sinx)n-2 (n-1)cos2x - e-x(sinx)n-1cosx]
write cos2x = 1 - sin2x and expand this integral ∫e-x(sinx)n-1cosx]using by parts..take cosx as second function..
At last u will get the relation
In + (n-1)In + In/n = (n-1)In-2
put n = 10 and u will get the relation 101I10/I8 = 90
