The value of `lim_(x->0)int_0^x(tln(1+t))/(t^4+4)dt`

The value of lim_(x rarr0)int_(0)^(x)(t ln(1+t))/(t^(4)+4)dt

The value of (lim)_(x->0)1/(x^3)int_0^x(t ln(1+t))/(t^4+4)dt is a. 0 b. 1/(12) c. 1/(24) d. 1/(64)

The value of lim_(x->0) cosec^4 x int_0^(x^2) (ln(1 +4t))/(t^2+1) dt is

The value of lim_(x to 0)(int_(0)^(x^(2))sec^(2)t dt)/(x sin x) is equal to -

The value of lim_(xrarr0)(int_0^(x^2) cos(t^2)dt)/(xsinx) is

The value of lim_( x to 0) (int_(0)^(x) sin t^(2) dt) / x^(2) is

The value of lim_(x rarr0)(int_(0)^(x) xe^(t^(2))dt)/(1+x-e^(x)) is equal to

Let f be a non-negative function in [0, 1] and twice differentiate in (0, 1). If int_0^x sqrt(1-(f'(t))^(2))dt=int_0^x f(t)dt , 0 lexle1 and f(0)=0 then the value of lim_(x to0)int_0^xf(t)/x^2 dt is