Explanation Given information: ∫ 0 π / 2 cos x d x , n = 10 . Explanation: To find exact value of the integral ∫ 0 π / 2 cos x d x using TI-84 calculator use the steps given below. Step 1: Press [MATH] and press 9 to access fnInt. Step 2: Press number 0 as a lower limit and Press [ALPHA] [^] to get π then press [ ÷ ] and a number 2 as an upper limit. Step 3: Press [COS] [ALPHA] [STO>]. It will look likes: ∫ 0 π / 2 cos x d _ Step 4: In front of d enter ALPHA] [STO>]. It will look likes: ∫ 0 π / 2 cos x d x Step 5: Press [ENTER] to get the final answer as 1 . Thus, the exact value of ∫ 0 π / 2 cos x d x is 1 . Midpoint Rule: The format for midpoint rule used on TI-84 is sum ( seq ( f ( x ) ) , X , a + Δ x 2 , b − Δ x 2 , Δ x ) ⋅ Δ x For ∫ 0 π / 2 cos x d x , n = 10 , Δ x = b − a n = π 2 − 0 10 = π 20 Start point: a + Δ x 2 = 0 + π / 20 2 = π 40 End point: b − Δ x 2 = π 2 − π / 20 2 = π 2 − π 40 = 19 π 40 To approximate the value of the integral ∫ 0 π / 2 cos x d x using TI-84 follow the below steps: Step 1: Press [2 nd ][STAT] to access LIST then go to [MATH] and then press 5 . Step 2: Press [2 nd ][STAT] to access LIST then go to [OPS] and then press 5 to get seq the page. Fill the below parameters by pressing [ENTER] : EXpr:cos ( x ) Variable:X Start: π 40 End: 19 π 40 Step: π 20 Paste Step 3: Move the cursor on “Paste” and Press [ENTER] and complete the bracket using [ )]. The output will display on a screen like: sum ( seq , ( cos ( x ) , X , π 40 , 19 π 40 , π 20 ) ) Step 3: Press 2 ND and press (-) to get Ans and then multiply it by π 20 The final input will look like sum ( seq , ( cos ( x ) , X , π 40 , 19 π 40 , π 20 ) ) ∗ π 20 . Step 4: Press [ENTER] to get the final answer as ≈ 1.001028824 . Thus, ∫ 0 π / 2 cos x d x ≈ 1.001028824 by using the Midpoint rule. Find error using the formula: | Approximated value - Actual value | . ⇒ | 1.001028824 − 1 | ⇒ 0.001028824 Thus, error using midpoint rule is 0.001028824

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 9.4, Problem 38E

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The approximate value of the integral ∫0π/2cos x dx by using the Midpoint rule, the Trapezoidal rule and Simpson’s rule with n = 10 then find the exact value by integration. Find the error for each approximation.

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Chapter 9.4, Problem 37E

Chapter 9.4, Problem 39E

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The approximate value of the integral ∫ 0 π / 2 cos x d x by using the Midpoint rule, the Trapezoidal rule and Simpson’s rule with n = 10 then find the exact value by integration . Find the error for each approximation.

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The approximate value of the integral ∫0π/2cos x dx by using the Midpoint rule, the Trapezoidal rule and Simpson’s rule with n = 10 then find the exact value by integration. Find the error for each approximation.

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