Int int y dx dy over the triangle with vertices (−1, 0), (0, 2), and (2, 0).?

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Answer 1 · 2017-12-19T18:05:07

See below.

We have #dS = Delta x(y) dy#

here #(Delta x(y))/bar(AB) = (H-y)/H# or

#Deltax(y) = bar(AB)/H(H-y)#

and then

#S = int_0^H y Delta x(y) dy = int_0^H bar(AB)/H(H-y)ydy= 1/6bar(AB) H^2#

enter image source here

The figures are left as an exercise to the reader

Here

#bar(AB) = 3# and #H = 2#