State Mean value theorem for integrals  

Suppose f(x) is a function that satisfies below conditions:

1. f(x) is Continuous in [a,b]
2. f(x) is Differentiable in (a,b)

Then, there exists a number c, s.t. a < c < b and

f(b) – f(a) = f ‘(c) (b – a)

Suppose f(x) is a function that satisfies below conditions:

1. f(x) is continuous in [a,b]
2. f(x) is Differentiable in [a,b)

Then, there exists a number c, s.t. a < c < b and

f(b) – f(a) = f ‘(c) (b – a)

Suppose f(x) is a function that satisfies below conditions:

1. f(x) is continuous in [a,b]
2. f(x) is Differentiable in (a,b)

Then, there exists a number c, s.t. a < c < b and

f(b) + f(a) = f ‘(c) (b – a)

Suppose f(x) is a function that satisfies below conditions:

1. f(x) is Continuous in (a,b)
2. f(x) is Differentiable in (a,b)

Then, there exists a number c, s.t. a < c < b and

f(b) – f(a) = f ‘(c) (b – a)