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

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 ?
 

Grade:12

1 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
9 years ago
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)

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