Explanation Formula used: Trapezoidal rule: ∫ a b f ( x ) d x ≈ h 2 ( y 0 + 2 y 1 + ⋯ + 2 y n − 1 + y n ) , where h = b − a n . Calculation: The given function is ∫ 0 2 4 − x 2 d x = π , n = 8 . Divide the interval from x = 0 to x = 2 into eight intervals. The height of the interval is, h = 2 − 0 8 = 2 8 = 0.25 Thus, the sub-intervals are: 0 , 0.25 , 0.5 , 0.75 , 1 , 1.25 , 1.50 , 1.75 , 2 . Find the values of y 0 , y 1 , ⋯ and tabulate as follows. n x n y n 0 0 4 − 0 2 = 2 1 0.25 4 − ( 0.25 ) 2 = 1.984 2 0.5 4 − ( 0.5 ) 2 = 1.936 3 0.75 4 − ( 0.75 ) 2 = 1.854 4 1 4 − ( 1 ) 2 = 1.732 5 1.25 4 − ( 1

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Chapter 25.5, Problem 18E

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To approximate: The value of the integral ∫024−x2dx=π,n=8 by using the trapezoidal rule and compare the result with π.

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Chapter 25.5, Problem 17E

Chapter 25.5, Problem 19E

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To approximate: The value of the integral ∫ 0 2 4 − x 2 d x = π , n = 8 by using the trapezoidal rule and compare the result with π .

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To approximate: The value of the integral ∫024−x2dx=π,n=8 by using the trapezoidal rule and compare the result with π.

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Chapter 25 Solutions