PLEASE WRITE CLEARLY 11. Find the length of the curve y =128x*1

To find the length of the curve we use formula ∫ab1+dydx2dxGiven y=x612+18x4 take derivative for y…

Answered: x° 1. Find the length of the curve y=;…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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PLEASE WRITE CLEARLY

1
1. Find the length of the curve y =
12
8x*
1<x<2.

Expert Solution

Step 1

To find the length of the curve we use formula

$\int_{a}^{b} \sqrt{1 + {(\frac{d y}{d x})}^{2}} d x G i v e n y = \frac{x^{6}}{12} + \frac{1}{8 x^{4}}$

take derivative for y

$y = \frac{x^{6}}{12} + \frac{1}{8 x^{4}} \frac{d y}{d x} = \frac{x^{5}}{2} - \frac{1}{2 x^{5}}$

Step 2

Replace the derivative inside the formula

$\int_{a}^{b} \sqrt{1 + {(\frac{d y}{d x})}^{2}} d x \frac{d y}{d x} = \frac{x^{5}}{2} - \frac{1}{2 x^{5}} \int_{1}^{2} \sqrt{1 + {(\frac{x^{5}}{2} - \frac{1}{2 x^{5}})}^{2}} d x \int_{1}^{2} \sqrt{1 + {({(\frac{x^{5}}{2})}^{2} - 2 \frac{x^{5}}{2} \cdot \frac{1}{2 x^{5}} + {(\frac{1}{2 x^{5}})}^{2})}^{2}} d x \int_{1}^{2} \sqrt{\frac{1}{2} + \frac{x^{10}}{4} + \frac{1}{4 x^{10}}} d x$

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