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# Find the exact length of the curve.$y = \displaystyle \frac{x^3}{3} + \displaystyle \frac{1}{4x}$ , $1 \le x \le 2$

## $\frac{59}{24}$

#### Topics

Applications of Integration

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### Video Transcript

Hey, it's clear. Someone new right here. So we have lying is equal to X cube over three plus one over four X. We're first going to find the derivative. So do you. Why, over DX We got X squared minus one over four X square. Afterwards, we're gonna square. So we get. Do you want? Over. Deac Square is equal to X square minus one over four square square. Um, excuse us X to the fourth minus one, huh? Plus won over 16. Next to the fourth. Now, when we plug it into our arc length equation, yeah, l is equal to from 1 to 2 square root of one plus next to the fourth minus one have plus one over 16 x to the fourth DDX. This becomes X to the fourth plus one Have plus one over 16 x to the fourth. This could be factored into X square plus one over four. Next square square. So when you put it into our equation comes from 1 to 2 square root of X square, plus one over four x square square. The this equals 59 over 24. Yeah,

#### Topics

Applications of Integration

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