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

1 Answer
Mar 13, 2018

Answer:

#"35 Joule"#

Explanation:

Small work done by force for a small distance #dx# is given by

#dW = F.dx#

Total work done is

#W = intdW = intF.dx#

#W = int_2^3(2x^3 + x)dx#

#W = [(2x^4)/4 + x^2/2]_2^3#

#W = [x^4/2 + x^2/2]_2^3#

#W = 1/2[x^4 + x^2]_2^3#

#W = 1/2[(3^4 - 2^4) + (3^2 - 2^2)] = "35 Joule"#