If `f(x)={{:(2x^(2)+1,"where "x lt1),(4x^(3)+1,"where "x gt1):}`, then `int_(0)^(2)f(x)dx` is-

If f(x)={(2x^(2)+1",", x le1),(4x^(3)-1",",x gt 1):} , then int_(0)^(2)f(x)dx is

If f(x)={(x,"when "0le x le 1),(2x-1,"when "x gt 1):} then -

Let f(x)={{:(int_(0)^(x)|1-t|dt,"where "xgt1),(x-(1)/(2),"where "xle1):} , then

Let f(x)={{:(1-x,0lexle1,),(0,1lexle2,),((2-x)^(2),2lexle3,):} , then 6int_(0)^(3)f(x)dx is equal to-

A function F(x) is defined as follows: F(x)={:{(1+2x,"when "xle1),(3-2x,"when "x gt1):} Determine F(0), F(-1.5),F(1), F(2.6) and F(x+2).

If f(x)={0 ,where x=n/(n+1),n=1,2,3.... and 1 else where then the value of int_0^2 f(x) dx is

If f (x) ={{:(x",", "when " 0 lt x lt 1),(2-x",", "when" 1 lt x le 2):} then f'(1) is equal to-

If f(x) ={(x^(3)", " x lt1),(2x-1", " x ge 1):} " and " g(x)={(3x", " x le2),(x^(2)", " x gt 2):} " then find " (f-g)(x).

If f(x)=|x-1|+|x+1| , then evaluate int_(-2)^(2)f(x)dx .

If for non-zero x,af(x)+bf((1)/(x))=(1)/(x)-5 where aneb , then find int_(1)^(2)f(x)dx .