Evaluate ∫10π0([sec−1x]+[cot−1x])dx, where [.] denotes the greatest integer function.
A
10π−cot1
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B
10π−sec1
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C
10π−tan1
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D
10π−sec1−tan1
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Solution
The correct option is C10π−sec1 Here, I=∫10π0([sec−1x]+[cot−1x])dx =∫sec10([sec−1x]+[cot−1x])dx+∫10πsec1([sec−1x]+[cot−1x])dx =∫sec10(0+0)dx+∫10πsec1(1+0)dx =0+(x)10πsec1=10π−sec1