What are the possible values of x for the following functions? F(x)=2-x / x(x-1)
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Answer:
16.5 square units
Step-by-step explanation:
You are expected to integrate the function between x=1 and x=4:
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<em>Additional comment</em>
If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.
The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.
This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...
area = 4.5 +3×4 = 16.5 . . . square units
The graph of the region is attached. The coordinates of the centroid are (5/3, 1).
The coordinates of the centroid are found by averaging the coordinates of the region;
Oₓ = (Aₓ+Bₓ+Cₓ)/3 = (0+1+4)/3 = 5/3
O(y) = (A(y) + B(y) + C(y)) = (0+3+0)/3=3/3=1
The coordinates of the centroid are found by averaging the coordinates of the region;
Oₓ = (Aₓ+Bₓ+Cₓ)/3 = (0+1+4)/3 = 5/3
O(y) = (A(y) + B(y) + C(y)) = (0+3+0)/3=3/3=1