(a) Explanation Given: The region bounded by y = x 2 and y = − x 2 − 4 x Calculation: Consider the graph provided in the text book. Use the Washer Method, V = ∫ a b π [ { f ( x ) } 2 − { g ( x ) } 2 ] d x ” The vertical strip is shown as follows: Outer radius will be, f ( x ) = − x 2 − 4 x And, the inner radius will be, g ( x ) = x 2 Compute the intersection points of two curves as follows: x 2 = − x 2 − 4 x 2 x 2 + 4 x = 0 2 x ( x + 2 ) = 0 x = 0 , − 2 So, the interval for the solid will be [ < (b) To determine To setup: an integral for the volume of the solid formed about the y -axis

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 6.2, Problem 36PS

(a)

To determine

To setup: an integral for the volume of the solid formed about the x -axis

(b)

To determine

To setup: an integral for the volume of the solid formed about the y -axis

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Chapter 6.2, Problem 35PS

Chapter 6.2, Problem 37PS

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3. <3 in Find the volume of solid obtained by rotating a region bounded by y = x and y = x³ the first quadrant. The region is rotated about the x-axis. [Hint: Go methodically. Graph in calculator, draw on paper, calculate intersection point analytically, show the washer on paper, write volume of washer, now integrate].

23. The region bounded by the curve 4y = x, the line x = 4 and the line y = 1, is rotated through 360° about the x-axis. Find the volume of the solid formed. 24. The area bounded by the curve y = 15kx – 15x and the x-axis is rotated through 360° about the x-axis, where k is an integer. The volume of - the solid formed is 240r. Find the value of k.

Chapter 6 Solutions

Student's Solution and Survival Manual for Calculus

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To setup: an integral for the volume of the solid formed about the x -axis

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Chapter 6 Solutions