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Integral 0 to 102 [tan^-1]dx [X] is the largest integer not exceeding x

Integral 0 to 102 [tan^-1]dx [X] is the largest integer not exceeding x

Grade:12th pass

1 Answers

Aditya Gupta
2075 Points
3 years ago
just put tan inverse x = y
or x= tany
or dx=sex^2ydy
now integral becomes 
0 to tan inverse(102) [y]sec^ydy
split this integral as 0 to 1 + 1 to tan inverse(102)
from 0 to 1 [y]=0
from 1 to tan inverse(102), [y]=1
so, answer is 102-tan1

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