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Question

If Φ(x)=dxsin12x cos72x, then Φ(π4)Φ(0)=

A
125
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B
95
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C
65
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Solution

The correct option is A 125
tan x=tsec2 x dx=dt f(x)=dxsin12xcos12x.cos4x=(1+tan2 x)sec2 xtan xdx =(1+t2)tdt=(t1/2+t3/2)dt =2t1/2+25t5/2=2tan x+25(tan x)5/2 ϕ(π4)ϕ(0)=2+25=125

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