Question Number 149415 by abdurehime last updated on 05/Aug/21

show that ∫_0 ^∞ (((sint−tcost)/t^3 ))^2 dt=(Π/(15))

Commented byabdurehime last updated on 05/Aug/21

please help me????

Answered by mindispower last updated on 05/Aug/21

byart =[−(1/5)(((sin(t)−tcos(t))^2 )/(t^5 ))] +(2/5)∫_0 ^∞ (((sin(t)−tcos(t))sin(t))/t^4 )dt =(2/5)[(((sin(t)−tcos(t))sin(t))/(−3t^3 )) ]_0 ^∞ +(2/(15))∫_0 ^∞ (((sin(t)cos(t)−tcos(2t)))/t^3 )dt =(1/(15))[((sin(t)cos(t)−tcos(2t))/(−t^2 ))]_0 ^∞ +(1/(15))∫_0 ^∞ ((2tsin(2t))/t^2 ) =(1/(15))∫_0 ^∞ ((sin(2t).2dt)/t)=(2/(15))∫_0 ^∞ ((sin(x)dx)/x)=(2/(15)).(π/2)=(π/(15))

Commented byabdurehime last updated on 05/Aug/21

please show me step by step

Commented bymnjuly1970 last updated on 05/Aug/21

very nice sir power...beavo..

Commented bymindispower last updated on 05/Aug/21

thanx sir