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Beyond Horizon Set 2 Paper 1 · Q20

Paper 1CalculusTrigonometry

Let

f(x)=(tan⁡x)3/2−3tan⁡x+tan⁡xf(x)=(\tan x)^{3/2}-3\tan x+\sqrt{\tan x}

Consider the three integrals

I1=∫01f(x) dx,I2=∫0.31.3f(x) dx,I3=∫0.51.5f(x) dxI_1=\int_0^1f(x)\,dx,\quad I_2=\int_{0.3}^{1.3}f(x)\,dx,\quad I_3=\int_{0.5}^{1.5}f(x)\,dx

Then,

AI1>I2>I3I_1>I_2>I_3
BI2>I1>I3I_2>I_1>I_3
CI3>I1>I2I_3>I_1>I_2
DI1>I3>I2I_1>I_3>I_2
EI2>I3>I1I_2>I_3>I_1
FI3>I2>I1I_3>I_2>I_1

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