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Question

Evaluate 10π0([sec1x]+[cot1x])dx, where [.] denotes the greatest integer function.

A
10πcot1
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B
10πsec1
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C
10πtan1
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D
10πsec1tan1
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Solution

The correct option is C 10πsec1
Here, I=10π0([sec1x]+[cot1x])dx
=sec10([sec1x]+[cot1x])dx+10πsec1([sec1x]+[cot1x])dx
=sec10(0+0)dx+10πsec1(1+0)dx
=0+(x)10πsec1=10πsec1

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