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Numerade Educator

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Problem 45 Hard Difficulty

Find the length of the curve
$ y = \displaystyle \int_1^x \sqrt{t^3 - 1}\ dt $ $ 1 \le x \le 4 $

Answer

$L=12.4$

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Video Transcript

it's clear someone you read here. So we're given that y is equal to into girl from one that's t cubed minus one d t. So we're gonna use the 1st 1 The mental theory, um, of calculus. Do you want over The ex is equal to D over the sex, huh? Wanting to create from one office t cubed minus one d t just equal to x cubed minus one. So we're gonna find the length of the curve. Just plug it into the formula one plus spirit of X cubed minus one square E X. This becomes equal Thio. We integrate 1 to 4 square of excuse deep pecs. This is equal to 124 next to the three. How's the nets? Which is equal to two X to the five house over four over five 14 which is equal to well, point for