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integrate [sin2x] from 0 to 2pi where [.] means greatest integer function

integrate [sin2x] from 0 to 2pi
where [.] means greatest integer function

Grade:12

2 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago
If the value of sin 2x is between 0 to 1, then [.] = 0
If the value of sin 2x is between -1 to 0, then [.] = -1.
sin 2x is negative in range : (pi/2,pi) and (3pi/2,2pi)
Hence, answer is : -1(pi-pi/2) -1(2pi - 3pi/2)
Answer : -pi
Thanks
Bharat Bajaj
IIT Delhi
askiitians faculty
vaanya
18 Points
7 years ago
thanku sir

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