12. To celebrate Pi Day, you want to approximate a to within 0.001.4Use the fact that a = 4 arctan(1)-dx to determine the smallest integer n needed toа.2+x*4approximate a by using the trapezoid rule, with the required accuracy. Hint: if f(x)1+x?then f"(x) <8 on the interval [0,1].

12. To celebrate Pi Day, you want to approximate ,r to within 0.001. a). Use the factpi= 4…

12. To celebrate Pi Day, you want to approximate a to within 0.001. 1 4 - dx to determine the smallest integer n needed to 1+x? a. Use the fact that ↑ = 4 arctan(1) 4 approximate by using the trapezoid rule, with the required accuracy. Hint: if f(x)= 1+x? then f"(x) < 8 on the interval [0,1].

12. To celebrate Pi Day, you want to approximate a to within 0.001. 1 4 - dx to determine the smallest integer n needed to 1+x? a. Use the fact that ↑ = 4 arctan(1) 4 approximate by using the trapezoid rule, with the required accuracy. Hint: if f(x)= 1+x? then f"(x) < 8 on the interval [0,1].

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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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.

Question

12. To celebrate Pi Day, you want to approximate a to within 0.001.
4
Use the fact that a = 4 arctan(1)
-dx to determine the smallest integer n needed to
а.
2
+x*
4
approximate a by using the trapezoid rule, with the required accuracy. Hint: if f(x)
1+x?
then f"(x) <8 on the interval [0,1].

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