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Q.

If a>0,∫0∞e−axcosbxdx=

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a

aa+b

b

1ab

c

aa2+b2

d

ba2+b2

answer is C.

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Detailed Solution

I=Re∫0∞e−ax⋅eibx⋅dx=Ree(−a+ib)x−a+ib|0∞                                        =Re1a−ib                                        =Re(a+iba2+b2)=aa2+b2
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