Home
Class 12
MATHS
Let f(x) be a continuous function and I ...

Let `f(x)` be a continuous function and `I = underset(1)overset(9)intsqrt(x)f(x) dx`, then

A

`[1/k]gt 5`

B

`1/8 [1/k]epsilon[0,1]`

C

`kepsilon(0,1/5)`

D

`1/(2k)+1` is an odd number

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D

`|int_(0)^(9)f(x)dx|=|a int_(0)^(1)f(at)dt|le 1/8 M`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) be a continuous function and I = int_(1)^(9) sqrt(x)f(x) dx , then

If a function y=f(x) such that f'(x) is continuous function and satisfies (f(x))^(2)=k+underset(0)overset(x)int [{f(t)}^(2)+{f'(t)}^(2)]dt,k in R^(+) , then find f(x)

Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x/7 AA x in R, then f(42) is

Let [x] denote the integral part of x in R and g(x) = x- [x] . Let f(x) be any continuous function with f(0) = f(1) then the function h(x) = f(g(x) :

Let f(x) be a continuous function in R such that f(x)+f(y)=f(x+y) , then int_-2^2 f(x)dx= (A) 2int_0^2 f(x)dx (B) 0 (C) 2f(2) (D) none of these

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(x) be real valued continuous function on R defined as f(x)=x^(2)e^(-|x|) then f(x) is increasing in

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

Let f(x) be a continuous function in R such that f(x) does not vanish for all x in R . If int_1^5 f(x)dx=int_-1^5 f(x)dx , then in R, f(x) is (A) an even function (B) an odd function (C) a periodic function with period 5 (D) none of these

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in R . If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to