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8. a) Define two partition P1 and P2 of ] [ such that 2, 5 P1 ⊂ P2 . Find the upper and lower product sums with respect to f , defined by ⎩ ⎨ ⎧ − ≥ < = 1 x , x 4 x, x 4 f(x) 2 . Also verify the relationship between these 4 sums. (4) b) Derive a reduction formula for ∫( n x) dx, m∈N m l . Hence evaluate ∫( n x) dx 4 l . (4) c) Find the approximate value of 5/3 ( upto 3 decimal places.
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