The force applied against a moving object travelling on a linear path is given by #F(x)= 2x^3+6x#. How much work would it take to move the object over #x in [2, 3] #?

1 Answer
Jan 28, 2016

Answer:

#W=47.5J#

Explanation:

Work, is an integral of force over distance, that is
#W=\intF(x)dx#

Here, #F(x)=2x^3+6x#
So, integrating #F(x)# with respect to #x# from #2# to #3#,
#int_2^3F(x)dx=\int_2^3(2x^3+6x)dx=(\frac{2x^4}{4}+\frac{6x^2}{2})|_2^3=\frac{3^4-2^4}{2}+3(3^2-2^2)#

Solving the above equation gives you the answer provided above.