show-that-0-sint-tcost-t-3-2-dt-15-

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

show that \int_{0}^{\infty} {(\frac{sint - tcost}{t^{3}})}^{2} dt = \frac{Π}{15}

Commented by abdurehime last updated on 05/Aug/21

please help me ? ? ? ?

Answered by mindispower last updated on 05/Aug/21

b y a r t

= [- \frac{1}{5} \frac{{(s i n (t) - t c o s (t))}^{2}}{t^{5}}]

+ \frac{2}{5} \int_{0}^{\infty} \frac{(s i n (t) - t c o s (t)) s i n (t)}{t^{4}} d t

= \frac{2}{5} {[\frac{(s i n (t) - t c o s (t)) s i n (t)}{- 3 t^{3}}]}_{0}^{\infty} + \frac{2}{15} \int_{0}^{\infty} \frac{(s i n (t) c o s (t) - t c o s (2 t))}{t^{3}} d t

= \frac{1}{15} {[\frac{s i n (t) c o s (t) - t c o s (2 t)}{- t^{2}}]}_{0}^{\infty} + \frac{1}{15} \int_{0}^{\infty} \frac{2 t s i n (2 t)}{t^{2}}

= \frac{1}{15} \int_{0}^{\infty} \frac{s i n (2 t) . 2 d t}{t} = \frac{2}{15} \int_{0}^{\infty} \frac{s i n (x) d x}{x} = \frac{2}{15} . \frac{π}{2} = \frac{π}{15}

Commented by abdurehime last updated on 05/Aug/21

please show me step by step

Commented by mnjuly1970 last updated on 05/Aug/21

v e r y n i c e s i r p o w e r \dots b e a v o . .

Commented by mindispower last updated on 05/Aug/21

t h a n x s i r