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 [0, 5] ?

Oct 26, 2017

see below

Explanation:

for a variable force

Work done=int_a^b(F(x)dx

in this case

Work done$= {\int}_{0}^{5} \left({x}^{2} + {e}^{x}\right) \mathrm{dx}$

$= {\left[\frac{1}{3} {x}^{3} + {e}^{x}\right]}_{0}^{5}$

$= {\left[\frac{1}{3} {x}^{3} + {e}^{x}\right]}^{5} - {\left[\frac{1}{3} {x}^{3} + {e}^{x}\right]}_{0}$

$= \frac{1}{3} {5}^{3} - {e}^{5} - 0 - {e}^{0}$

$= \frac{125}{3} - 1 - {e}^{5}$

$= \left(\frac{122}{3} - {e}^{5}\right) J$