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What is the arc length of the curve given by #f(x)=1+cosx# in the interval #x in [0,2pi]#?

Answer 1

Christopher Allers

The arc length is most nearly #7.64# units.

Recall that arc length is given by #A = int_a^b sqrt(1 + (dy/dx)^2) dx#.

The derivative of #f'(x)# is #f'(x)= -sinx#.

#A = int_0^(2pi) sqrt(1 + (-sinx)^2)dx#

#A = int_0^(2pi) sqrt(1 + sin^2x)#

An approximation using a calculator gives #A = 7.64#.

Hopefully this helps!

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Answer 2

William Abdalla

The arc length of the curve given by ( f(x) = 1 + \cos(x) ) in the interval ( x ) in ([0, 2\pi]) is ( 2\pi ).

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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.