What is the arc length of $f (x) = - x sin x + x cos (x - \frac{π}{2})$ $f(x)=-xsinx+xcos(x-pi/2)$ on $x \in [0, \frac{π}{4}]$ $x in [0,(pi)/4]$ ?

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Answer 1 · 2018-03-21T13:34:10

$\frac{π}{4}$ $pi/4$

The arc length of $f (x)$ $f(x)$ , $x \in [a . b]$ $x in[a.b]$ is given by:
$S_x=int_b^af(x)sqrt(1+f'(x)^2)dx$

$f(x)=-xsinx+xcos(x-pi/2)=-xsinx+xsinx=0$
$f'(x)=0$

Since we just have $y=0$ we can just take the length of s straight line between $0to pi/4$ which is $pi/4-0=pi/4$

What is the arc length of f(x)=-xsinx+xcos(x-pi/2) f(x)=−xsinx+xcos(x−π2)f(x)=-xsinx+xcos(x-pi/2) on x in [0,(pi)/4]x∈[0,π4]x in [0,(pi)/4]?