`Let f(x)=x^(2)-3x+2` be a function `AA x in R` Then the area bounded by the curve `|f(|x|)| `between `1<=|x|<=2` and the x -axis is `(A) (1)/(5) sq.units (B) (1)/(4) sq.units (C) (1)/(3) sq.units (D) (1)/(6) sq.Units`

Let f(x) be a continuous function such that the area bounded by the curve y=f(x), the x-axis, and the lines x=0 and x=a is 1+(a^(2))/(2)sin a. Then,

Let f (x) = x^(3)-3x ^(2)+3x+1 and g be the inverse of it , then area bounded by the curve y = g (x) wirth x-axis between x =1 to x=2 is (in square units):

Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R , then

Let f(x)="max"{sin x,cos x,1/2} , then determine the area of region bounded by the curves y=f(x) , X-axis, Y-axis and x=2pi .

Let f(x)=x-x^(2) and g(x)=ax . If the area bounded by f(x) and g(x) is equal to the area bounded by the curves x=3y-y^(2) and x+y=3 , then find the value of |[a]| : [Note: denotes the greatest integer less than or equal to k.]

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)=x^(2)-x+1, AA x ge (1)/(2) , then the solution of the equation f(x)=f^(-1)(x) is

Let f(x) be a continuous function, AA x in R, f(0) = 1 and f(x) ne x for any x in R , then show f(f(x)) gt x, AA x in R^(+)

Let f be a real - valued function defined on R ( the set of real numbers) such that f(x) = sin^(-1) ( sin x) + cos^(-1) ( cos x) The area bounded by curve y = f(x) and x- axis from pi/2 le x le pi is equal to

Let f(x)=2x+1. AA x in R , then the solution of the equation f(x)=f^(-1)(x) is