What is the arc length of $f (t) = (t - t \sqrt{t - 1}, 8 - 2 t)$ $f(t)=(t-tsqrt(t-1),8-2t)$ over $t \in [1, 4]$ $t in [1,4]$ ?

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Answer 1 · 2018-06-23T10:30:35

$7.26345$ $7.26345$

we have
$x (t) = t - t \sqrt{t - 1}$ $x(t)=t-tsqrt(t-1)$
then
$x'(t)=1-sqrt(t-1)-t/(2sqrt(t-1))$

$y'(t)=-2$

so we have to solve

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

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