# 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,pi/12 ] #?

The formula provides the work.

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To calculate the work done to move the object over the given interval, we need to integrate the force function F(x) with respect to x over the interval [0, π/12].

∫[0,π/12] (sin(x) + 1) dx

= [-cos(x) + x] evaluated from 0 to π/12

= [-cos(π/12) + π/12] - [-cos(0) + 0]

= [-cos(π/12) + π/12] - [-1 + 0]

= -cos(π/12) + 1 + π/12 ≈ 0.962 units of work

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