# 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 ] #?

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

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To find the work done, integrate the force function F(x) over the interval [1,3] with respect to x:

∫[1 to 3] (3x^2 + x) dx

= [x^3 + (1/2)x^2] evaluated from 1 to 3

= [(3^3 + (1/2)(3^2)) - (1^3 + (1/2)(1^2))]

= [(27 + 9/2) - (1 + 1/2)]

= [27 + 9/2 - 1 - 1/2]

= 27 + 9/2 - 1 - 1/2

= 27 + 4.5 - 1 - 0.5

= 30 - 2

= 28 units of work.

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