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On a hot summer afternoon, engineers study how heat distributes along a new metal alloy rod. Let T(x) be the temperature in °C at a point x cm from one end of the rod, where 0≤x≤2. The temperature gradient satisfies
and it is observed T(2)=10.
Find T(x).
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Find the average temperature Tˉ along the rod from x=0 to x=2.
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