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

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

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

If y=int_(0)^(x)(t^(2))/(sqrt(t^(2)+1))dt then rate of change of y with respect to x when x=1 is

lim_(xrarr0) (int_(0)^(x)(t^(2))/(sqrt(a+t))dt)/(x-sinx)=1(agt0) . Then the value of a is

Let f(x)=int_(0)^(x)(t^(2))/(sqrt(1+t^(2)))backslash dt. Then int_(1)^(2)(1)/({f'(x)}^(2))backslash dx equals

Given that lim_(x to oo)(int_(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1 , then find the values of a and b.

I=int_(0)^(-1)(t ln t)/(sqrt(1-t^(2)))dt=

lim_(x to 0)(int_(0)^(x^(2))(tan^(-1)t)dt)/(int_(0)^(x^(2))sin sqrt(t)dt) is equal to :

If f(x)=int_(0)^(x){f(t)}^(-1)dt and int_(0)^(1){f(t)}^(-1)=sqrt(2)

If int_(0)^(x^(2)) sqrt(1=t^(2)) dt, then f'(x)n equals