Question

The force applied against a moving object travelling on a linear path is given by `F(x)= 2x^3+x`. How much work would it take to move the object over `x in [2, 4]`?

Answer 1

126J

Explanation:

Provided it's a conservative force

`W = int_(x_1)^(x_2) Fdx`

`= int_2^4 (2x^3 + x)dx = [1/2x^2(x^2+ 1)]_2^4`

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

`=8(17) - 2(5) = 126`