Let $f(x)=(\tan x)^\frac32-3\tan x+\sqrt{\tan x}$. Consider the integrals $$I_1=\int_0^1f(x)dx$$ $$I_2=\int_{0.3}^{1.3}f(x)dx$$ $$I_3=\int_{0.5}^{1.5}f(x)dx$$ Then, prove that $I_1>I_3>I_2$
I found $f'(x)$ but it is not very straight-forward on how to determine the exact nature of the function. My idea to compare the area under curve rather than explicitly evaluate the integral.
How to go about it?
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