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 [1,3 ] #?

2 Answers
Mar 3, 2018

here,work will be done against the force to move the object,

so,work done #dW =F dx# (as,angle between #F# and #dx# is zero,as moving along a linear pathway)

so, #dW =(3x^2 +x)dx#

or, #dW =3x^2 dx +x dx#

so, #int _0^W = 3 int_1^3 x^2dx + int_1^3 x dx#

so, #W=[x^3]_1^3 + 1/2 [x^2]_1^3=30J#

Mar 3, 2018

Answer:

#W = 30# J

Explanation:

Simply integrate using the bounds provided:
#W = \int_1^3 F(x)dx#

#= \int_1^3 (3x^2+x) dx#

#=3\int_1^3x^2 dx + \int_1^3xdx#

#= (x^3+1/2x^2)_(x=1)^(x=3)#

#=27+9/2-(1+1/2)#

#=30# J