Question

Question #8be27

Answer 1

See bellow.

Explanation:

Supposing `f(x)` continuous at `x_0`

`lim_(delta->0)1/(2delta)int_(x_0-delta)^(x_0+delta) f(x)dx = lim_(delta->0)(F(x_0+delta)-F(x_0-delta))/((x_0+delta)-(x_0-delta)) =f(x_0)`

Applying this result to each integral in sequence we will arrive to the expected result.