\int\limits^4_3{x^(2)-x } \, dx help

Question

`\int\limits^4_3{x^(2)-x } \, dx` help

Answer 1

`(53)/(6)`

Explanation:

`\int\limits^4_3 {x^2-x} \, dx`

= [
`(x^3)/(3)` -
`(x^2)/(2)` ] ← evaluate for upper limit - lower limit

= (
`(64)/(3)` -
`(16)/(2)` ) - (
`(27)/(3)` -
`(9)/(2)` )

=
`(64)/(3)` - 8 - 9 +
`(9)/(2)`

=
`(155)/(6)` - 17

=
`(53)/(6)`