`y=f(x)` is a function which satisfies `f(0)=0, f"''(x)=f'(x)` and `f'(0)=1` then the area bounded by the graph of `y=f(x)`, the lines `x=0, x-1=0` and `y+1=0` is

y=f(x) is a function which satisfies (i) f(0)=0 (ii) f^prime prime(x)=f^prime(x) and (iii) f^prime(0)=1 then the area bounded by the graph of y=f(x) , the lines x=0, x-1=0 and y +1=0 , is

A function y=f(x) satisfying f'(x)=x^(-(3)/(2)),f'(4)=2 and f(0)=0 is

There exists a function f(x) satisfying 'f (0)=1,f(0)=-1,f(x) lt 0,AAx and

Let f(x) be a real valued function satisfying the relation f(x/y) = f(x) - f(y) and lim_(x rarr 0) f(1+x)/x = 3. The area bounded by the curve y = f(x), y-axis and the line y = 3 is equal to

Let f(x) be a real valued function satisfying the relation f(x/y) = f(x) - f(y) and lim_(x rarr 0) f(1+x)/x = 3. The area bounded by the curve y = f(x), y-axis and the line y = 3 is equal to

Let f(x) be a real valued function satisfying the relation f((x)/(y))=f(x)-f(y) and lim_(x rarr0)(f(1+x))/(x)=3. The area bounded by the curve y=f(x), y-axis and the line y=3 is equal to

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then

Let f(x)={{:(2^([x]),, x lt0),(2^([-x]),,x ge0):} , then the area bounded by y=f(x) and y=0 is