Step 1 Take the direct antiderivative using the Power Rule for Integration. (x + 2)² When n-4. Ar Stap 3 (x + 2)² Stap 2 Apply the Trapezoidal Rule, let n-4. Step 5 Ax- As n 4 ✓ (x + 2)² dx- F(x) dx -✓ 3 ₁-[ = 1 Substitute these values in the Trapezoidal Rule. 2 dx = Here a 3x X 0.3333✔ X 24 1/4 Ax- 1/2 ✔ 3/4 (0✔ (1/2 , therefore the corresponding x values are the following. (3/4✔ (✔ 3352 ✔ Therefore, we have the following. 2 25 121 9 0.3333 (rounded to four decimal places) 2 Therefore, the value of the given integral obtained by using the Trapezoidal Rule is 3352 ✔ + Stap 4 Now use Simpson's Rule, which states the following. Tole(x) ](x) - (₂) (...)+(x) 1/4 + 2)2 +2) 1/2 + 2)² 3/4 3/4 +212 1+2) 32 32 0.3352 (rounded to four decimal places) 1x x and fx) - 2 0.3352
Step 1 Take the direct antiderivative using the Power Rule for Integration. (x + 2)² When n-4. Ar Stap 3 (x + 2)² Stap 2 Apply the Trapezoidal Rule, let n-4. Step 5 Ax- As n 4 ✓ (x + 2)² dx- F(x) dx -✓ 3 ₁-[ = 1 Substitute these values in the Trapezoidal Rule. 2 dx = Here a 3x X 0.3333✔ X 24 1/4 Ax- 1/2 ✔ 3/4 (0✔ (1/2 , therefore the corresponding x values are the following. (3/4✔ (✔ 3352 ✔ Therefore, we have the following. 2 25 121 9 0.3333 (rounded to four decimal places) 2 Therefore, the value of the given integral obtained by using the Trapezoidal Rule is 3352 ✔ + Stap 4 Now use Simpson's Rule, which states the following. Tole(x) ](x) - (₂) (...)+(x) 1/4 + 2)2 +2) 1/2 + 2)² 3/4 3/4 +212 1+2) 32 32 0.3352 (rounded to four decimal places) 1x x and fx) - 2 0.3352
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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