Question

If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______

Options

• `13/2`

• `17/2`

• `21/2`

• `27/2`

Answer 1

If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is `underline(17/2)`.

Explanation:

`int_-2^3 |x - 2| dx`

= `int_-2^2 |x - 2|dx + int_2^3|x - 2|dx`

= `int_-2^2-(x - 2)dx + int_2^3(x - 2)dx`

= `int_-2^2 x dx + 2int_-2^2 dx + int_2^3 x dx - 2int_2^3 dx`

= `-[x^2/2]_-2^2 + 2[x]_{-2}^2 + [x^2/2]_2^3 - 2[x]_2^3`

= `-1/2[(2)^2 - (-2)^2] + 2[2 - (-2)] + 1/2(9 - 4) - 2(3 - 2)`

= `17/2`