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What is the arc length of #f(x)=xsinx-cos^2x # on #x in [0,pi]#?

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Aug 16, 2017

The arc length #s# of a function #f(x)# on #x in[a,b]# is given by

#s=int_a^bsqrt(1+(f'(x))^2)dx#

Here, #f(x)=xsinx-cos^2x# so #f'(x)=sinx+xcosx+2cosxsinx#.

Then, the arc length in question is given by:

#s=int_0^pisqrt(1+(sinx+xcosx+2cosxsinx)^2)dxapprox6.4705#

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