To determine Calculate the length of the curve. Explanation Given information: The equation of curve is y = x 1 2 − 1 3 x 3 2 . The curve lies from x = 1 to x = 4 . Calculation: Show the equation of curve as follows: y = x 1 2 − 1 3 x 3 2 (1) Differentiate Equation (1) with respect to x . d y d x = d d x ( x 1 2 − ( 1 3 ) x 3 2 ) = 1 2 x 1 2 − 1 − 1 3 × 3 2 x 3 2 − 1 = 1 2 x − 1 2 − 1 2 x 1 2 = 1 2 x 1 2 − 1 2 x 1 2 Take square on both sides. ( d y d x ) 2 = ( 1 2 x 1 2 − 1 2 x 1 2 ) 2 = ( 1 2 x 1 2 ) 2 + ( 1 2 x 1 2 ) 2 − 2 × 1 2 x 1 2 × 1 2 x 1 2 = 1 4 x + x 4 − 1 2 = 1 4 ( 1 x − 2 + x ) The expression to find the length of the curve y = f ( x ) on the interval [ a , b ] is as follows: L = ∫ a b 1 + ( d y d x ) 2 d x Substitute 1 4 ( 1 x − 2 + x ) for ( d y d x ) 2 , 1 for a , and 4 for b

Thomas' Calculus Format: Unbound (saleable) With Access Card

14th Edition

ISBN: 9780134768762

Author: Hass, Joel R.^heil, Christopher D.^weir, Maurice D.

Publisher: Prentice Hall

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Chapter 6, Problem 19PE

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Calculate the length of the curve.

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