Let `f(x)=int_(x)^(0) g(t)dt,`where g is a non -zero even function . If f(x+5)=g(x),then `int_(x)^(0) (t)dt,` equal

Let f ( x) = int _ 0 ^ x g (t) dt , where g is a non - zero even function . If f(x + 5 ) = g (x) , then int _ 0 ^ x f (t ) dt equals :

Let f ( x) = int _ 0 ^ x g (t) dt , where g is a non - zero even function . If f(x + 5 ) = g (x) , then int _ 0 ^ x f (t ) dt equals :

Let g(x) = int_(x)^(2x) f(t) dt where x gt 0 and f be continuous function and 2* f(2x)=f(x) , then

Let g(x)=int_(0)^(x)f(t)dt where fis the function whose graph is shown.

For the function f(x)=int_(0)^(x)(sin t)/(t)dt where x>0

Let f:R rarr R be defined asble f(x)=int_(0)^(x)(sin^(2)t+1)dt and g is the inverse function of f, than g'((3 pi)/(4)) is equal to

If f(x) is differentiable function and f(x)=x^(2)+int_(0)^(x) e^(-t) (x-t)dt ,then f)-t) equals to

If f(t) is an odd function, then int_(0)^(x)f(t) dt is -

f(x)=int_(0)^(x)g(t)log_(e)((1-t)/(1+t))dt ,where "g" is a continuous odd function. If int_(-pi/2)^( pi/2)(f(x)+(x^(2)cos x)/(1+e^(x)))dx=((pi)/(alpha))^(2)-alpha ,then alpha is equal to