Explanation Given Information: The provided functions are y = sec 2 x 4 and y = 4 − x 2 for x = − 1 to x = 1 . Formula used: Write the formula of definite integral of ∫ a b sec 2 u d u . ∫ a b sec 2 n u d u = [ tan n u n ] a b Here, n is the any number. Write the formula of definite integral of ∫ a b sin u d u . ∫ a b u n d u = [ u n + 1 n + 1 ] a b Write the formula of definite integral of ∫ a b d u . ∫ a b d u = [ u ] a b Graph: Draw area bounded by graph of y = sec 2 x 4 and y = 4 − x 2 for x = − 1 to x = 1 . Consider provided function. y = sec 2 x 4 At x = − 1 , y x = − 1 = sec 2 ( − 1 4 ) = 1.065 At x = 0 , y x = 0 = sec 2 ( 0 4 ) = sec 2 0 = 1 At x = 1 , y x = 1 = sec 2 ( 1 4 ) = 1.065 Now, the table for ordered pair ( x , y ) for the function y = sec 2 x 4 is shown below: x y − 1 1.065 0 1 1 1.065 Again, consider provided function. y = 4 − x 2 At x = − 1 , y x = − 1 = 4 − ( − 1 ) 2 = 3 At x = 0 , y x = 0 = 4 − ( 0 ) 2 = 4 At x = 1 , y x = 1 = 4 − ( 1 ) 2 = 3 Now, the table for ordered pair ( x , y ) for the function y = 4 − x 2 is shown below: x y − 1 3 0 4 1 3 Thus, the resulting graph of y = sec 2 x 4 and y = 4 − x 2 for x = − 1 to x = 1 is, Calculation: From above graph, the area bounded by the graph of y = sec 2 x 4 and y = 4 − x 2 for x = − 1 to x = 1 can be calculated as, ∫ − 1 1 [ ( 4 − x 2 ) − ( sec 2 x 4 ) ] d x = 2 ∫ 0 1 [ ( 4 − x 2 ) − ( sec 2 x 4 ) ] d x Rewrite

10th Edition

ISBN: 8220101426222

Author: Larson

Publisher: CENGAGE L

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Chapter 8.5, Problem 56E

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To graph: The area bounded by the graph of y=sec2x4 and y=4−x2 for x=−1 to x=1.

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Chapter 8.5, Problem 55E

Chapter 8.5, Problem 57E

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Chapter 8 Solutions

EBK CALCULUS: AN APPLIED APPROACH

Ch. 8.1 - For each angle, find a coterminal angle such that...Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 1SWU Ch. 8.1 - Prob. 2SWU Ch. 8.1 - Prob. 3SWU Ch. 8.1 - Prob. 4SWU Ch. 8.1 - Prob. 5SWU Ch. 8.1 - Prob. 6SWU

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To graph: The area bounded by the graph of y = sec 2 x 4 and y = 4 − x 2 for x = − 1 to x = 1 .

Solution Summary: The solution is 5.291square unit. Write the formula of definite integral of

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To graph: The area bounded by the graph of y=sec2x4 and y=4−x2 for x=−1 to x=1.

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Chapter 8 Solutions