B&Auml;&deg;LKENT COMPLEX CALCULUS2

# B&Auml;&deg;LKENT COMPLEX CALCULUS2 - Date Saturday...

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Date: April 21, 2007, Saturday NAME:. .................................................... Time: 14:00-16:00 ¨ STUDENT NO:. .................................................... Math 206 Complex Calculus – Midterm Exam II – Solutions 1 2 3 4 TOTAL 25 25 25 25 100 Please do not write anything inside the above boxes! PLEASE READ: Check that there are 4 questions on your exam booklet. Write your name on the top of every page. A correct answer without proper reasoning may not get any credit. Q-1) Evaluate the integral Z 0 x ln x x 3 + 1 dx . Hint: You may use the fact that Z 0 x x 3 + 1 dx = 2 π 3 9 . Answer: Let α = e iπ/ 3 , choose constants 0 < ρ < 1 < R , and consider the path γ = L 1 + C R + L 2 + C ρ in C where; z L 1 means z = x for ρ x R , z C R means z = Re for 0 θ 2 π/ 3, z ∈ - L 2 means z = α 2 x for ρ x R , and z ∈ - C ρ means z = ρe for 0 θ 2 π/ 3. Let

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B&Auml;&deg;LKENT COMPLEX CALCULUS2 - Date Saturday...

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