Consider the improper integrals \(\rm I=\int_{\pi/2}^{\pi}\frac{1}{\sqrt{\sin x}}dx\) and for a ≥ 0 \(\rm I_a=\int_{a}^\infty\frac{1}{x\sqrt{1+x^3}}dx\)
1
The integral I is convergent
2
The integral I is not convergent
3
The integral Ia converges for a = \(\frac{1}{2}\) but not for a = 0
4
The integral Ia converges for all a ≥ 0