TS EAMCET 5 May 2018 Shift 1 Solved Paper

The integration is expressed as,
In =

∞

∫

π∕2

e−xcosnx dx
Integrate the above integral by parts,
In=[−e−xcosnx]π∕2∞ −

∞

∫

π∕2

−e−x.ncosn−1x(−sin‌x)dx
=0−

∞

∫

π∕2

ne−xcosn−1x‌sin‌x‌d‌x
Again apply the integration by parts in the above integral,
In=−n2In+n(n−1)In−2
In(n2+1)=n(n−1)In−2

In

In−2

=

n(n−1)

n2+1

Substitute n = 2018 in the above equation,

I2018

I2016

=

2018(2017)

20182+1