Question

The force applied against a moving object travelling on a linear path is given by `F(x)= x^2+e^x`. How much work would it take to move the object over `x in [3,7]`?

Answer 1

Work=Force x distance = Fx. However, the force is changing with x (i.e. F is a function of x), so integration should be used to solve this problem. Do this and you'll find:
Work = 1181.9 J

Explanation:

Work=Force x distance = Fx. However, the force is changing with x (i.e. F is a function of x), so integration should be used to solve this problem. By doing this you're taking the work done over tiny (i.e. infinitesimally small) steps in x and summing them all up to get the total work.

`F(x) = x^2 + e^x`

To find the work done integrate F(x) between the limits 3 and 7:

Work = `int_3^7x^2 + e^x dx` joules

Work = `[x^3/3 + e^x]_3^7` J
Work = `(7^3 / 3 + e^7)-(3^3 / 3 + e^3)` J
Work = `7^3 / 3 + e^7 - 3^2 - e^3` J
Work = 1181.9 J