prove-that-1-0-lt-0-pi-4-x-tan-x-dx-lt-pi-2-32-2-1-2-lt-pi-4-pi-2-sin-x-x-dx-lt-2-2-3-0-lt-100pi-200pi-cos-x-x-dx-lt-1-100pi-

Question Number 12826 by malwaan last updated on 03/May/17

prove that

1 : 0 < \int_{0}^{\frac{π}{4}} x \sqrt{\tan x} dx < \frac{π^{2}}{32}

2 : \frac{1}{2} < \int_{\frac{π}{4}}^{\frac{π}{2}} \frac{\sin x}{x} dx < \frac{\sqrt{2}}{2}

3 : 0 < \int_{100 π}^{200 π} \frac{\cos x}{x} dx < \frac{1}{100 π}