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

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Answer 1 · 2018-04-13T05:05:27

The arc length is most nearly $7.64$ $7.64$ units.

Recall that arc length is given by $A = \int_{a}^{b} \sqrt{1 + {(\frac{d y}{d x})}^{2}} d x$ $A = int_a^b sqrt(1 + (dy/dx)^2) dx$ .

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!

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