Let `f"[0,oo)rarr R` be a continuous and stricity increasing function such that `f^(3) (x) = underset(0)overset(x)inttf^(2)(t) dt, x ge0`.
The area enclosed by `y = f(x)` , the x-axis and the ordinate at `x = 3` is ` "_______"`

Let f"[0,oo)rarr R be a continuous and stricity increasing function such that f^(3) (x) =int_(0)^(x) tf^(2)(t) dt, x ge0 . The area enclosed by y = f(x) , the x-axis and the ordinate at x = 3 is "_______"

Let f:[0,oo)rarr R be a continuous strictly increasing function,such that f^(3)(x)=int_(0)^(x)t*f^(2)(t)dt for every x>=0. Then value of f(6) is

Let f:R rarr R be a differentiable and strictly decreasing function such that f(0)=1 and f(1)=0. For x in R, let F(x)=int_(0)^(x)(t-2)f(t)dt

Let f:(0,oo)R be a continuous,strictly increasing function such that f^(3)(x)=int_(0)^(0)tf^(2)(t)dt. If a normal is drawn to the curve y=f(x) with gradient (-1)/(2), then find the intercept made by it on the y-axis is 5(b)7(c)9(d)11

Let y = g(x) be the inverse of a bijective mapping f : R rarr R f(x) = 3x^(3) + 2x . The area bounded by graph of g(x), the x-axis and the ordinate at x = 5 is

Let f : R to R be a continuous function satisfying f(x)+underset(0)overset(x)(f)"tf"(t)"dt"+x^(2)=0 for all "x"inR . Then-

The area the region enclosed by f(x)=x^(3)-10x and g(x)=6x, x ge 0, y ge 0 is

Let f : [-1, 2]to [0, oo) be a continuous function such that f(x)=f(1-x), AA x in [-1, 2] . If R_(1)=int_(-1)^(2)xf(x)dx and R_(2) are the area of the region bounded by y=f(x), x=-1, x=2 and the X-axis. Then :