Math Problem Statement

find the error in trapezoidal approximation T10 for integral 1 to 2 11e^1/x dx

Solution

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Math Problem Analysis

Mathematical Concepts

Numerical Integration
Trapezoidal Rule
Error Estimation
Exponential Functions

Formulas

Trapezoidal Rule: T_n = (b - a) / (2n) * [f(a) + 2 * Σ f(x_i) + f(b)]
Error Formula for Trapezoidal Rule: E_T = -((b - a)^3 / (12n^2)) * f''(ξ)

Theorems

Error Bound in Numerical Integration
Trapezoidal Approximation Theorem

Suitable Grade Level

Undergraduate Mathematics or Advanced High School Calculus

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