Question

The force applied against a moving object travelling on a linear path is given by `F(x)= cosx + 2`. How much work would it take to move the object over `x in [ 0, (3 pi) / 8 ]`?

Answer 1

`W=sin((3pi)/8)+(6pi)/8`

Explanation:

`W=int _0^(3pi/8) (cos x+2) d x`
`W=[sin x+2x]_0^(3pi/8)`
`W=[sin (3pi/8)+2(3pi/8)]-[sin 0+2*0]`
`W=[sin (3pi/8)+2(3pi/8)]-[0]`
`W=[sin (3pi/8)+2(3pi/8)]`
`W=sin((3pi)/8)+(6pi)/8`