1.

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

Answer»

F( c) for some `c in (0,2)`
2F (c ) for some `c in (0,2)`
f.(c ) for some `c in (0,1) `
NONE of these

Solution :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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