Explanation Formula used: Integration by parts: “If u and v are differentiable functions, then ∫ u d v = u v − ∫ v d u .” Area under the curve: The area under the curve y = f ( x ) and x from a to b is, Area= ∫ a b f ( x ) d x . Calculation: According to the given data, the Area = ∫ 1 3 x 3 ( x 2 − 1 ) 1 3 d x . Solve the integral by the method of integration by parts. Let u = x 2 and d v = x ( x 2 − 1 ) 1 3 d x . Then, d u d x = 2 x d u = 2 x d x ∫ d v = ∫ x ( x 2 − 1 ) 1 3 d x = 1 2 ∫ ( x 2 − 1 ) 1 3 d ( x 2 − 1 ) v = 3 8 ( x 2 − 1 ) 4 3 Substitute the corresponding values in the above formula ∫ u d v = u v − ∫ v d u and simplify. ∫ x 3 ( x 2 − 1 ) 1 3 d x = 3 8 x 2 ( x 2 − 1 ) 4 3 − 3 4 ∫ x ( x 2 − 1 ) 4 3 d x = 3 8 x 2 ( x 2 − 1 )

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, Problem 25RE

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To find: The area between y=x3(x2−1)13 and x-axis from x=1 to x=3 .

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Chapter 8, Problem 24RE

Chapter 8, Problem 26RE

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Chapter 8 Solutions

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 area between y = x 3 ( x 2 − 1 ) 1 3 and x -axis from x = 1 to x = 3 .

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To find: The area between y=x3(x2−1)13 and x-axis from x=1 to x=3 .

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Chapter 8 Solutions