Explanation Given information: ∫ 0 1 2 x e x 2 d x , n = 10 . Explanation: To find exact value of the integral ∫ 0 1 2 x e x 2 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 1 as an upper limit. Step 3: Enter a number 2 then [ALPHA] [STO>] [2 nd ] [ ÷ ] [^][ALPHA] [STO>] [^] 2 . It will look likes: ∫ 0 1 2 x e x 2 d _ Step 4: In front of d enter ALPHA] [STO>]. It will look likes: ∫ 0 1 2 x e x 2 d x Step 5: Press [ENTER] to get the final answer as 1.718281828 . Thus, the exact value of ∫ 0 1 2 x e x 2 d x is 1.718281828 . 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 1 2 x e x 2 d x , n = 10 , Δ x = b − a n = 1 − 0 10 = 1 10 = 0.1 Start point: a + Δ x 2 = 0 + 1 / 10 2 = 1 20 = 0.05 End point: b − Δ x 2 = 1 − 1 / 10 2 = 1 − 1 20 = 1 − 0.05 = 0.95 To approximate the value of the integral ∫ 0 1 2 x e x 2 d x using TI-84 follow the below steps: Step 1: From the home screen press [2 nd ][STAT] to access LIST then go to [MATH] and press. Step 2: Press [2 nd ][STAT] to access LIST then go to [OPS] and press 5 to get seq the page Fill the below parameters by pressing [ENTER]: EXpr: 2 x e x 2 Variable:X Start: 0.05 End: 0.95 Step: 0.1 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 ( 2 x e x 2 , X , 0.05 , 0.95 , 0.1 ) ) Step 3: Press 2 ND and press (-) to get Ans and then multiply it by 0.1 . The final input will look like sum ( seq ( 2 x e x 2 , X , 0.05 , 0.95 , 0.1 ) ) ∗ 0.1 Step 4: Press [ENTER] to get the final answer as ≈ 1.712342989 . Thus, ∫ 0 1 2 x e x 2 d x ≈ 1.712342989 by using the Midpoint rule. Find error using formula: | Approximated value - Actual value | ⇒ | 1.712342989 − 1.718281828 | ⇒ | − 0.005938839 | . ⇒ 0.005938839 Thus, error using Midpoint rule is 0.005938839 . Trapezoidal Rule: The format for trapezoidal rule used on TI-84 is ( Calculate first term saperately + sum ( seq ( 2 f ( x ) ) , X , a + Δ x , b − Δ x , Δ x ) + Calculate second term saperately ) ⋅ Δ x 2 For ∫ 0 1 2 x e x 2 d x , n = 10 , Δ x = b − a n = 1 − 0 10 = 0

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus & Its Applications

15th Edition

ISBN: 9780137590469

Author: Larry Goldstein / David Lay

Publisher: Pearson Education (US)

See similar textbooks

Videos

Question

Chapter 9.4, Problem 40E

To determine

The approximate value of the integral ∫012xex2dx by using the Midpoint rule, Trapezoidal rule and Simpson’s rule with n = 10 then find the exact value by integration .Find error for each approximation.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.4, Problem 39E

Chapter 9.4, Problem 41E

Students have asked these similar questions

The function f is given by f(x) = cos(x + 1). The solutions to which 6 of the following equations on the interval 0≤ x ≤ 2 are the solutions to f(x) = 1½ on the interval 0 < x < 2π? 2 A √√3 cos x - sin x = 1 B √√3 cos x + sin x = 1 C √3 sin x COS x = 1 D √√3 sin x + cos x = 1

Suppose that the graph below is the graph of f'(x), the derivative of f(x). Find the locations of all relative extrema, and tell whether each extremum is a relative maximum or minimum. Af'(x) Select the correct choice below and fill in the answer box(es) within your choice. (Simplify your answer. Use a comma to separate answers as needed.) -10 86-4-2 -9- B 10 X G A. The function f(x) has a relative maximum at x= relative minimum at x = and a B. The function f(x) has a relative maximum at x= no relative minimum. and has C. There is not enough information given. D. The function f(x) has a relative minimum at x= no relative maximum. and has E. The function f(x) has no relative extrema.

K Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. f(x) = 12x+13x 12/13 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. OA. There are no relative maxima. The function has a relative minimum of (Use a comma to separate answers as needed.) OB. There are no relative minima. The function has a relative maximum of (Use a comma to separate answers as needed.) OC. The function has a relative maximum of at x= (Use a comma to separate answers as needed.) OD. There are no relative extrema. at x= at x= and a relative minimum of at x=

Chapter 9 Solutions

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus & Its Applications

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The approximate value of the integral ∫ 0 1 2 x e x 2 d x by using the Midpoint rule, Trapezoidal rule and Simpson’s rule with n = 10 then find the exact value by integration .Find error for each approximation.

Solution Summary: The author explains how to determine the approximate value of the integral displaystyle 'underset'0overset1int, using the TI-84 calculator.

Videos

The approximate value of the integral ∫012xex2dx by using the Midpoint rule, Trapezoidal rule and Simpson’s rule with n = 10 then find the exact value by integration .Find error for each approximation.

Want to see the full answer?

Chapter 9 Solutions