Question

Set up an integral that represents the length of the curve. then use your calculator to find the length correct to four decimal places. x = y − 2y, 1 ≤ y ≤ 4

Answer 1

If your function is

... x = f(y) = y - 2^y

then its derivative is

... f'(y) = 1 - ln(2)·2^y

and the integral is

$\displaystyle\int_1^4{\sqrt{1+f'(t)^{2}}}\,dt\approx 11.6900$

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If numerical integration is being done, it is convenient to let the calculator use the numerical derivative (f'(t)). The same result is obtained as with the explicit derivative function (1-ln(2)2^t).