Explanation Formula used: The volume of the solid formed by rotating R about the x axis is ∫ a b π f ( x ) 2 d x , where R is the region between f ( x ) and x -axis from x = a to x = b . Calculation: Calculate the volume of the solid when the region R is rotating about the- x axis. Here, f ( x ) = 2 − x 2 intersects y = 0 . Therefore, 2 − x 2 = y 2 − x 2 = 0 x 2 = 2 x = ± 2 Here, R is the region between f ( x ) = 2 − x 2 and x axis where x varies from − 2 to 2 . Substitute the respective values in ∫ a b π f ( x ) 2 d x and evaluate. V = ∫ − 2 2 π ( 2 − x 2 ) 2 d x = ∫ − 2 2 π ( 2 2 + ( x 2 ) 2 − 2 ( 2 ) ( x ) ) d x = ∫ − 2 2 π ( 4

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 8.2, Problem 18E

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To find: The volume of the solid of revolution formed when its rotating about the x axis where the region bounded by the curves f(x)=2−x2 , y=0 .

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Chapter 8.2, Problem 17E

Chapter 8.2, Problem 19E

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Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

Ch. 8.1 - YOUR TURN 1 Find Ch. 8.1 - YOUR TURN 2 Find Ch. 8.1 - YOUR TURN 3 Find Ch. 8.1 - YOUR TURN 4 Find . Ch. 8.1 - YOUR TURN 5 Find Ch. 8.1 - Prob. 1WE Ch. 8.1 - Find the following. W2. Ch. 8.1 - Find the following. W3. Ch. 8.1 - Find the following. W4. Ch. 8.1 - Use integration by parts to find the integrals in...

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The volume of the solid of revolution formed when its rotating about the x axis where the region bounded by the curves f ( x ) = 2 − x 2 , y = 0 .

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To find: The volume of the solid of revolution formed when its rotating about the x axis where the region bounded by the curves f(x)=2−x2 , y=0 .

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Chapter 8 Solutions