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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 ] #?

Answer 1

Nathan Ashcroft

The formula provides the work.

#W=int_0^(pi/12) F(x)dx=int_0^(pi/12) (sinx+1)dx=0.30#

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Answer 2

William Audy

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.