# The force applied against a moving object travelling on a linear path is given by #F(x)= cosx + 2 #. How much work would it take to move the object over #x in [ 0, (13 pi) / 8 ] #?

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To find the work done, we need to integrate the force function ( F(x) ) over the given interval ([0, \frac{13\pi}{8}]) with respect to ( x ):

[ W = \int_{0}^{\frac{13\pi}{8}} \left( \cos(x) + 2 \right) , dx ]

[ W = \left[ \sin(x) + 2x \right]_{0}^{\frac{13\pi}{8}} ]

[ W = \left( \sin\left(\frac{13\pi}{8}\right) + 2\cdot\frac{13\pi}{8} \right) - \left( \sin(0) + 2\cdot0 \right) ]

[ W = \left( \sin\left(\frac{13\pi}{8}\right) + \frac{13\pi}{4} \right) - 0 ]

[ W = \sin\left(\frac{13\pi}{8}\right) + \frac{13\pi}{4} ]

[ W \approx -0.707 + 10.21 ]

[ W \approx 9.503 ]

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