2017-2018学年米一学湘《支西与积分支编潮一2 3.(10%)Use the Laplace transform to solve the IVP x"(t)=-4x(t)+sint.x(0)=x'(0)=0.. 5.(1%)Use the Residue Theorem toevaluate the integral 1+sin2 0 6.()Find the Fouier uransformof)6 X 4.(10%)Finda Mobius transformation f(z)whichmaps the real axis onto the unit circle and satisfies 0=2017-2018 学年第一学期《复变函数与积分变换》期终考试试卷--2 3. (10%) Use the Laplace transform to solve the IVP x t x t t x x   ( ) 4 ( ) sin , (0) (0) 0 = − + = = . 4. (10%) Find a Möbius transformation f(z) whichmapsthe real axis onto the unit circle and satisfies 1 ( ) 2 f i = . 5. (10%) Use the Residue Theorem to evaluate the integral 2 - d 1 sin    +   . 6. (10%) Find the Fourier transform of 4 ( ) 16 x f x x = +