Menu Close

Find-L-tcosh2t-

Tinku Tara 0 Comments
Pin




Question Number 16493 by Sai dadon. last updated on 23/Jun/17
Find L{tcosh2t}
FindL{tcosh2t}
Commented by prakash jain last updated on 23/Jun/17
∫_0 ^∞ tcosh 2te^(−st) dt =∫_0 ^( ∞) t((e^(2t) +e^(−2t) )/2)e^(−st) dt =(1/2)[∫_0 ^( ∞) te^((2−s)t) dt+∫_0 ^∞ te^(−(s+2)t) dt] =(1/2)[((te^((2−s)t) )/(2−s))−(e^((2−s)t) /((2−s)^2 ))−((te^(−(2+s)t) )/(2+s))−(e^(−(s+2)t) /((s+2)^2 ))]_0 ^∞ =(1/2)[(1/((2−s)^2 ))+(1/((2+s)^2 ))] =(((2+s)^2 +(2−s)^2 )/(2(s^2 −4)^2 ))=((s^2 +4)/((s^2 −4)^2 ))
∫0∞tcosh2te−stdt=∫0∞te2t+e−2t2e−stdt=12[∫0∞te(2−s)tdt+∫0∞te−(s+2)tdt]=12[te(2−s)t2−s−e(2−s)t(2−s)2−te−(2+s)t2+s−e−(s+2)t(s+2)2]0∞=12[1(2−s)2+1(2+s)2]=(2+s)2+(2−s)22(s2−4)2=s2+4(s2−4)2

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *