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What is the arc length of #f(t)=(t-tsqrt(t-1),8-2t) # over #t in [1,4]#?

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Jun 23, 2018

Answer:

#7.26345#

Explanation:

we have
#x(t)=t-tsqrt(t-1)#
then
#x'(t)=1-sqrt(t-1)-t/(2sqrt(t-1))#

#y'(t)=-2#

so we have to solve

#int_1^4sqrt((1-sqrt(t-1)-t/(2sqrt(t-1)))^2+4)dt#

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