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Let I1=∫π/6π/3 sin⁡xxdx,I2=∫π/6π/3 sin⁡(sin⁡x)sin⁡xdx and I3=∫π/6π/3 sin⁡(tan⁡x)tan⁡xdx Then arrange I1,I2 and I3 in the decreasing order of their values.

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a

I1>I2>I3

b

I2>I1>I3

c

I3>I2>I1

d

I1=I2=I3

answer is B.

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Detailed Solution

f(x)=sin⁡xx is a decreasing function and sin⁡xx>0 for all x in (0,π) . Since sin⁡xsin⁡xx>sin⁡(tan⁡x)tan⁡x for π6I1>I3

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Let I1=∫π/6π/3 sin⁡xxdx,I2=∫π/6π/3 sin⁡(sin⁡x)sin⁡xdx and I3=∫π/6π/3 sin⁡(tan⁡x)tan⁡xdx Then arrange I1,I2 and I3 in the decreasing order of their values.