Reference no: EM132288224

Analytic Function Theory Exercises -

1. Compute the integral ∫_∂D(0,8) dz/(1+e^z).

2. Compute the integral ₀∫^2π sin²t/(5+4cost) dt.

3. Compute the integral ₀∫^∞ cos(2x)/(x²+4) dx.

4. Compute the integral _-∞∫^∞ e^-ix/(x²+x+1) dx.

5. Compute the integral _-∞∫^∞ cos(ax)/(x²+a²) dx for all a > 0.

6. Compute the integral ₀∫^∞ dx/((x²+a²)(x²+b²)) for all a, b ∈ R such that 0 < a < b.

7. Compute the integral ₀∫^∞ sinx/(x(x²+1)) dx.

8. Compute the limit lim_{R→∞ -R}∫^R sinx/x dx.

9. Compute the integral ₀∫^∞ dx/(1+xⁿ) for all integers n ≥ 2.

Attachment:- Assignment File.rar