Question

How do you evaluate the definite integral `int root3(t)-2dt` from [-1,1]?

Answer 1

`int_(-1)^(1)(root3(t)-2 )dt`

Rewritten:
`=int_(-1)^(1)(t^(1/3)-2)dt`

`=[3/4t^(4/3)-2t]_(-1)^1`

`=(3/4(1)^(4/3)-2(1))-(3/4(-1)^(4/3)-2(-1))`

`=color(red)(3/4)-2color(red)(-3/4)-2`

`=-4`