Reference no: EM131004291
If f is a continuous function of two variables x ∈ R and y ∈ R, defined over some region D ∈R2, then the average value of f on D is given by
fav = 1/A ∫∫D f(x,y) dA,
where A is the area of the region D.
Use this definition of fav to answer the following questions.
Find the average value of y sin (xy) over the rectangle
R = {(x,y) : 0 ≤ x ≤ 1 ,0 ≤ y ≤ y ≤ π/2}
find the average of x2 + y2 over the triangle with vertices (0, 0), (1, 0), and (1, 1)
c. If the centroid of a region d is given by (x‾, y‾), where x‾ is the average value of x over d and y‾ is the average value of y over D, find the coordinates of the centroid of the region bounded by the curves y = 2x2 and y=12 - x2.
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