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Question

If the function g(t)=t22tcot11+x(1+t)2xdx, then g(5)g(3) is equal to ___.


  1. 5

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Solution

The correct option is A

5


g(t)=t22tcot11+x(1+t)2xdx (i)g(t)=t22tcot1(1+t)2x1+xdx (ii)
(i) + (ii) gives
2g(t)=t22t(π2)dxg(t)=π4((t1)21)g(5)g(3)=π4(15)π4(3)=5


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