Which of the following statements are true?

(i) \int_0^\infty x\sqrt{x} \ e^{-x^5} \, dx = \frac{\sqrt{\pi}}{5}

(ii) \int_0^\infty 4^{-3x^2} \, dx = \sqrt{\frac{\pi}{3 \ \ln 4}}

(iii) It is given that the n - dimensional volume of an n - dimensional ball of radius R is V_n(R) = \frac{\pi^{n/2} R^n}{\Gamma\left(\frac{n}{2} + 1\right)} then V_4(1) = \frac{\pi^{2}}{2} and V_5(1) = \frac{8\pi^{2}}{15}

(iv) Area under the curve defined by f(x) = x^{-1/2}(1 - x)^{-1/2} on the interval [0, 1] is given by \int_0^1 x^{-1/2}(1 - x)^{-1/2} \, dx then \int_0^1 x^{-1/2}(1 - x)^{-1/2} \, dx = \frac{\pi}{2}