Question

Question 12 Find the length of the curve defined by the parametric equations $x = t^2$, $y = t^3$, $0 \le t \le 1$ (in exact value, no decimal approximations) $\frac{13\sqrt{13}}{27} - \frac{8}{27}$ $\frac{13\sqrt{13}}{8} - \frac{27}{8}$ $\frac{13\sqrt{13}}{8} - 1$ None of the other choices none of the other choices 2 pts

          Question 12
Find the length of the curve defined by the parametric equations $x = t^2$, $y = t^3$, $0 \le t \le 1$ (in exact value, no decimal approximations)
$\frac{13\sqrt{13}}{27} - \frac{8}{27}$
$\frac{13\sqrt{13}}{8} - \frac{27}{8}$
$\frac{13\sqrt{13}}{8} - 1$
None of the other choices
none of the other choices
2 pts

Question 12
Find the length of the curve defined by the parametric equations x = t^2, y = t^3, 0 ≤ t ≤ 1 (in exact value, no decimal approximations)
(13√(13))/(27) - (8)/(27)
(13√(13))/(8) - (27)/(8)
(13√(13))/(8) - 1
None of the other choices
none of the other choices
2 pts

Added by Enrique B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

06/11/2023

Step 1

Step 1: The arc length of a parametric curve is given by: $$L = \int_{a}^{b} \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} dt$$ Show more…

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Question 12 Find the length of the curve defined by the parametric equations x= t², y= t³, 0 ≤ t ≤ 1 (in exact value, no decimal approximations) $\frac{13\sqrt{13}}{27}-\frac{8}{27}$ $\frac{13\sqrt{13}}{8}-\frac{27}{8}$ $\frac{13\sqrt{13}}{8}-1$ None of the other choices none of the other choices 2 pts