double integral x1xy dA r 01 x 01Solution Integrate first wi

Solution

Integrate first with respect to y: (0 to 1) integral x/(1 + xy) dy = [ln|1 + xy|](0 to 1) = [ln|1 + x*1|] - [ln|1 + x*0|] = ln|1 + x| Now, integrate with respect to x: (0 to 1) integral ln|1 + x| dx <--- use int by parts to solve = [(x + 1)ln|x + 1| - x](0 to 1) = [(1 + 1)ln|1 + 1| - 1] - [(0 + 1)ln|0 + 1| - 0] = 2ln(2) - 1 ˜ 0.386