calculate-D-x-2-y-dxdy-with-D-x-y-R-2-0-x-3-and-1-y-e-

Question Number 78700 by abdomathmax last updated on 20/Jan/20

c a l c u l a t e \int \int_{D} \frac{∣ x - 2 ∣}{y} d x d y w i t h

D = {(x, y) \in R^{2} / 0 ⩽ x ⩽ 3 a n d 1 ⩽ y ⩽ e}

Commented by john santu last updated on 20/Jan/20

= \int_{1}^{e} \int_{0}^{3} (\frac{∣ x - 2 ∣}{y}) d x d y

= \int_{1}^{e} \frac{(2 x - \frac{1}{2} x^{2}) ∣_{0}^{2} + (\frac{1}{2} x^{2} - 2 x) ∣_{2}^{3}}{y} d y

= \int_{1}^{e} \frac{2 + \frac{1}{2}}{y} d y = \frac{5}{2} (l n y) ∣_{1}^{e} = \frac{5}{2}