Answer to Question #319215 in Math for prathik ghosh

Question

MID_TERM ASSIGNMENT

1. Evaluate the integral ∫ (𝒛̅) 𝟐𝒅𝒛 𝟐+𝒊 𝟎 a) Along the line 𝒚 = 𝒙 𝟐 b) Along the real axis from 0 to 2 and then vertically 0 to 2+i

2. Use Cauchy’s Integral Formula to evaluate ∫ 𝒛𝒅𝒛 𝑪 𝒁𝟐−𝟑𝒛+𝟐 , where C is the circle |𝒛 − 𝟐| = 𝟏 𝟐

3. Evaluate ∬ √𝒚 𝟐 + 𝒛 𝟐 𝑹 𝒅𝒚𝒅𝒛; over the region R in the y-z planr bounded by 𝒚 𝟐 + 𝒛 𝟐 = 𝟒

4. Evaluate∭ (𝟐𝒙 + 𝒚)𝒅𝒗 𝑽 ; where V is closed by the cylinder 𝒛 = 𝟒 − 𝒙 𝟐 ;and the planes x=0;y=0;y=2 and z=0