Question

`\int\limits^2_1 {x^(2)-8x+8 } \, dx`

Answer 1

`{ \underline{ \sf{\int\limits^2_1 {x^(2)-8x+8 } \, dx} \: = \: - 1}}`

Explanation:

`{ \tt{\int\limits^2_1 {x^(2)-8x+8 } \, dx}} \\ \\ = { \tt{[ \frac{ {x}^(3) }{3} - 4 {x}^(2) + 8x ] {}^(2) _(1)}}`

Substitute x with the limits:

`= { \tt{( \frac{ {2}^(3) }{3} - 4( {2)}^(2) + 8(2)) - ( \frac{ {1}^(3) }{3} - 4( {1)}^(2) + 8(1)) }} \\ = { \tt{( (8)/(3) - (11)/(3) )}} \\ \\ = { \tt{ - 1}}`