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∫0π/219 cos x +12 sin x dx=

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a

log6

b

15log6

c

115log6

d

110log6

answer is C.

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Detailed Solution

I=∫0π/219Cos x+12Sin xdx =∫0π/21.(2dt1+t2)9(1−t21+t2)+12(2t1+t2)=∫012 dt9-9t2+24t =29∫01dt532-t-432 =291253log53-t+4353+t-4301 =115log6

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∫0π/219 cos x +12 sin x dx=