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

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1 Answer

Mar 21, 2018

#pi/4#

Explanation:

The arc length of #f(x)#, #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#

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