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Let f(x) be a differentiable function in...

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

A

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

B

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

C

f.(c ) for some `c in (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 `c in (0,2) rarr int_0^2 f(x)dx = 2f(c ) `, where `c in (0,2)`.
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