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Question

If π2<t<2π3 and =sin2t0dx4cos2tx2 then the value of 2005(I+t)π equals

A
2004
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B
2006
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C
2005
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D
None of these
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Solution

The correct option is C 2005
I=sin2t0dx(2cost)2x2={sin1(x2cost)}sin2t0
=sin1(sin2t2cost)=sin1(sint)=sin1(sin(πt))
(π2<t<2π3)
I=πt I+t=π(π3<πt<π2)
I+tπ=1
2005(I+t)π=2005

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