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

work done = #f*dx#
here F=#3*x^2+x#
substituting and integrating from 2 to 3 we get
W=#int_2^3(3x^2+x).dx#
w=#[x^3+x^2/2]_2^3# #[27+9/2]-[8+4/2]# #19+5/2# #43/2#=#21.5J#