`int_(0)^(oo)e^(-x^(2))dx=(sqrtpi)/(2)` then

If int_(0)^(oo)e^(-x^(2))dx=(sqrt(pi))/(2), then int_(0)^(oo)e^(-ax^(2))dx where a>0 is: (A)(sqrt(pi))/(2) (B) (sqrt(pi))/(2a)(C)2(sqrt(pi))/(a) (D) (1)/(2)(sqrt((pi)/(a)))

If int_(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int_(0)^(oo) e^(-ax^(2)) dx, a gt0 , s

int_(0)^(oo)x^(3)e^(-x^(2))dx=

int_(1)^(oo)x^(-(3/2))dx

If int_ (0)^(oo) e^(-x^(2)) dx = (sqrt (pi))/(2), and int_ (0)^(oo) e^(-ax^(2) ) dx, a> 0 is (i) (sqrt (pi))/(2) (ii) (sqrt (pi))/(2a) (iii) 2 (sqrt (pi))/(a) (iv) (1)/(2) sqrt ((pi)/(a))

int_(0)^(2)e^(-x)dx

int_(0)^(oo)(1)/(3+x^(2))dx

int_(0)^(oo)(a^(-x)-b^(-x))dx=

int_(0)^(oo)(a^(-x)-b^(-x))dx

Given that int_(-oo)^( oo)e^(-x^(2))dx=sqrt(pi) and f(t)=int_(-oo)^( oo)e^(-tx^(2))dx(t>0), then 2|(f'(t))/(sqrt(pi))times t^(3/2)| is