The force applied against a moving object travelling on a linear path is given by #F(x)= sinx + 1 #. How much work would it take to move the object over #x in [ 0, (5pi) / 3 ] #?

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Answer 1 · 2017-07-05T06:27:01

The work is=5.74J#

We need

#intsinxdx=-cosx+C#

The work done is

#W=F*d#

The work done is

#W=int_(0)^(5/3pi)(1+sinx)dx#

#=[x-cosx]_(0)^(5/3pi)#

#=(5/3pi-cos(5/3pi))-(0-cos0))#

#=(5/3pi+1-0.5)#

#=5.74J#