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

1 Answer
Apr 16, 2016

(3+e^2) units

Explanation:

Work done
Let the object move a distance dx.
Work done dw=-F(x).dx
-ve sign shows that force is being applied against the direction of motion. Total work done is integral of the expression within the stated limits.

w=-int_0^2F(x).dx=-int_0^2(2+e^x)dx
=-[2x+e^x]_0^2=-[(2xx2+e^2)-(2xx0+e^0)]
=-[(4+e^2)-(1)]
=-(3+e^2)
Work done in moving the object=3+e^2