# 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] #?

##### 1 Answer

Feb 13, 2016

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.

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

Work =

Work =

Work =

Work =

Work = 1181.9 J