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The difference between the greatest and the least values of the function `f(x) = int_0^x (at^2 + 1 + cost)dt, a > 0` for `x in [2, 3]` is

A

`(19)/(3)a+1+sin3-sin2`

B

`(18)/(3)a+1+2sin3`

C

`(18)/(3)a-1+2 sin3`

D

none of these

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The correct Answer is:
A
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