any one able to solve this problem?

[jani baadshah]

can anyone solve this problem me please??question is attached pdf.please reply with the detail
thanks in advance

 

[_Eduardo_]

Apply "Residue Theorem".

The example at Wikipedia is your problem ( Residue theorem - Wikipedia, the free encyclopedia ).

Note:

\[ \int_C \frac{e^{itz}}{z^2+1} \,\! {}\,dz=\int_C \frac{e^{itz}}{2i}\left(\frac{1}{z-i}-\frac{1}{z+i}\right)\,\!\,dz
{}=\int_C \frac{e^{itz}}{2i(z-i)} \,\!\,dz\]

because the pole at -i is outside C

 

[jani baadshah]

how residue theorem can be applied?
it is actualy inverse fourier transform

 

[jani baadshah]

well i have solved the problem using exponential integral