`int_(v_0)^0(dv)/(sqrt(v))=-alphaint_0^t dt`

int_(0)^(9)[sqrt(t)]dt

int_(0)^(9)[sqrt(t)]dt .

int_(0)^(1)t^(2)sqrt(1-t)*dt

The value of (int_(0)^(1)(dt)/(sqrt(1-t^(4))))/(int_(0)^(1)(1)/(sqrt(1+t^(4)))dt) is

The value of (int_(0)^(1)(dt)/(sqrt(1-t^(4))))/(int_(0)^(1)(1)/(sqrt(1+t^(4)))dt) is

The value of (int_(0)^(1)(dt)/(sqrt(1-t^(4))))/(int_(0)^(1)(1)/(sqrt(1+t^(4)))dt) is

int_(0)^(1)t^(5)*sqrt(1-t^(2))*dt

Let f be a non - negative function on the interval [0,1] . If int_(0)^(x)sqrt(1-(f'(t)))^(2)dt=int_(0)^(x)f(t)dt,0lexle1andf(0)=0 then

If f(x)=int_(0)^(x)(dt)/((f(t))^(2)) and int_(0)^(2)(dt)/((f(t))^(2))=(6)^((1)/(3)) then