P.o.t.W. #33 Solution
area of region =\displaystyle\int_0^1{x\arctan x\,{{d}}x} Apply integration by parts to find \int{x\arctan x\,{{d}}x} Let u = \arctan x , then du=\displaystyle\frac{1}{{{x^2} + 1}}\differentialD x\displaystyle ; and {{d}}v=x\,{{d}}x , then \displaystyle v=\frac{1}{2}{x^2} Hence,...