Home
Class 12
MATHS
Let f(x) be a differentiable function i...

Let f(x) be a differentiable function in the interval (0,2) then the value of `int_(0)^(2)f(x)` is

A

f(c )for some `cin(0,2)`

B

2f(c )for some `cin(0,2)`

C

f'(c )for some `cin(0,1)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let us consider a function `g(t)=int_(0)^(t)f(x)dx`
Now applying Lagrange’s Mean value theorem in (0,2)
`rArr(g(2)-g(0))/(2-0)=g'(c )`, where `cin(0,2)rArrint_(0)^(2)f(x)dx=2f(c ),` where `cin(0,2)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

Let f(x) be a differentiable function in the interval (0,2) , then the value of int_0^2 f(x) dx is :

Let f(x) be differentiate function symmetric about x=2 , then the value of int_(0)^(4)cos(pix)f'(x)dx is equal to________.

Let f:R to R be defined as f(x)=e^(-x)sinx . If F:[0, 1] to R is a differentiable function such that F(x)=int_(0)^(x)f(t)dt , then the vlaue of int_(0)^(1)(F'(x)+f(x))e^(x)dx lies in the interval

Let f(x) be a twice-differentiable function and f'(0)=2. The evaluate: lim_(x rarr0)(2f(x)-3f(2x)+f(4x))/(x^(2))

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

Let f(x) be twice differentiable function such that f'(0) =2 , then, lim_(xrarr0) (2f(x)-3f(2x)+f(4x))/(x^2) , is

Let f(x) be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then int_(0)^(1)f(x)dx=

If f(x) is differentiable and strictly increasing function,then the value of lim_(x rarr0)(f(x^(2))-f(x))/(f(x)-f(0)) is 1 (b) 0(c)-1 (d) 2