Trapezoidal Rule: Find T8 & M8 for ∫cos(x^2)dx from 1 to 0

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SUMMARY

The discussion focuses on calculating the approximations T8 and M8 for the integral of cos(x^2) from 1 to 0 using the Trapezoidal Rule. The user confirms that n=8, indicating the number of subintervals for the approximation. The proposed formula for the Trapezoidal Rule is T8 = (n/2) * [f(0) + f(0.2) + f(0.4) + f(0.6) + f(0.8) + f(1)], and the user intends to use a calculator in degree mode for calculations. This setup is correct for implementing the Trapezoidal Rule.

PREREQUISITES
  • Understanding of the Trapezoidal Rule for numerical integration
  • Basic knowledge of calculus, specifically integration techniques
  • Familiarity with evaluating functions at specific points
  • Ability to use a scientific calculator in degree mode
NEXT STEPS
  • Study the derivation and application of the Trapezoidal Rule
  • Learn about error analysis in numerical integration methods
  • Explore the Simpson's Rule for comparison with the Trapezoidal Rule
  • Practice calculating integrals using numerical methods with different values of n
USEFUL FOR

Students in calculus courses, educators teaching numerical methods, and anyone interested in approximating integrals using the Trapezoidal Rule.

pureouchies4717
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hey guys... i kinda forgot how to do this

question is: find the approximations T8 and M8 for integral of cos(x^2)dx from 1 to 0

now my question is whether or not that 8 means that n=8

and also, is this right?

id do the following:

n/2[f(0)+f(.2)+f(.4)+f(.6)+f(.8)+f(1)]

and id use the degree mode on my calculator

is that how i set it up?
 
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arg can someone help me? please
 

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