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Answer :
The value of F(10) - F(8) = 24 + 8 ln (7/5).
First, we need to find F(x) by integrating F '(x).
For this, let's use the partial fraction method as follows: ∫x² / (x - 3) dx = ∫(x-3+ 9) / (x-3) dx = ∫dx + ∫(9 / (x-3) dx = x + 9 ln |x-3| + C.
Now we can find F (10) and F (8) as follows:
F (10) = 10 + 9 ln |10-3| + C = 10 + 9 ln 7 + C
F (8) = 8 + 9 ln |8-3| + C = 8 + 9 ln 5 + C
Thus, F (10) - F (8) = (10 + 9 ln 7 + C) - (8 + 9 ln 5 + C) = 2 + 9 ln (7/5) = 2 + 8 ln (7/5) = 24 + 8 ln (7/5)
Therefore, the answer is b.
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