Question

How do you evaluate the definite integral `int dx` from `[12,20]`?

Answer 1

`int_12^20dx=8`

Explanation:

The definite integral `intdx` from `[12,20]` is written as

`int_12^20dx` or `int_12^20 1xxdx`

and as differential of `x` is `1`, `intdx=int1dx=x`

and `int_12^20dx=[x]_12^20=20-12=8`

Answer 2

`8`

Explanation:

`int_12^(20)1dx`

`=[x]_12^(20)`

`=20-12larr" upper - lower"`

`=8`

Answer 3

`8`

Explanation:

A definite integral (by its very definition) represents the area under the associated function, which in this case is the area under a straight line `y=1` between `x=12` and `x=20`, which is a rectangle.

Thus, using `A="base" xx "height"`:

`int_12^20 \ dx = (20-12)(1) = 8`