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.

Let f : (a, b) to R be twice differentiable function such that f(x) = int _(a) ^(x) g (t) dt for a differentiable function g(x) . If f(x) = 0 has exactly five distinct roots in (a,b) , then g(x) g'(x) = 0 has at least

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and STATEMENT 2 : g(x)=f'(x) is an even function , then f(x) is an odd function.

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and g(x)=f'(x) is an even function , then f(x) is an odd function.

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and STATEMENT 2 : g(x)=f'(x) is an even function , then f(x) is an odd function.

Let f(x)=int_2^x (dt)/sqrt(1+t^4) and g be the inverse of f . Then, the value of g'(0) is

Let f(x)=int_2^x (dt)/sqrt(1+t^4) and g be the inverse of f . Then, the value of g'(0) is

Let f(x) = int_2^(x) (dt)/(sqrt(1+t^(4))) and g be the inverse of f. Then g^('1)(0) =