The value of the constant a>0 such that∫a0[tan-1x^1/2]dx = ∫a0[cot-1x^1/2]dx where [.] represents greatest integer function, is ?

Hi,

See the grapgh of both tan^-11 and cot^-1
Now the integrations will be equal till the time gratest integer is giving zero. But cot^-1 starts from pi/2 and decreses and tan^-1 starts from 0 and increases so they will give zero when both gives values less than zero.

So the ans is a belongs to (cot1 to tan1)

Approved