Question

Let I_n = ∫|sin x|[sin x] dx for x ∈ [-2nπ,2nπ], where n ∈ N and [,] = GIF, find the value of In for ∑ ∈ [n = 1,100].

Answer 1

We have, 

= – 2n × 2 = – 4n

Now, 

= – 4(1 + 2 + 3 + ........... + 100) 

= – 4 × (100 × 101/2) 

= – 20200