Math Problem Statement
please use simpsons rule, trapezoid rule, and middle rule to approximate the integral from 0 to 2. THe integral is (^4√ (1+x^2)dx) with n = 8 and please give answers of 6 decimals places. The 4 isn't a muliplcation its the cubed root
Solution
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Math Problem Analysis
Mathematical Concepts
Numerical Integration
Approximation Techniques
Integral Calculus
Formulas
Trapezoidal Rule: T_n = (h / 2) * [f(x_0) + 2 * Σ f(x_i) + f(x_n)]
Midpoint Rule: M_n = h * Σ f((x_(i-1) + x_i) / 2)
Simpson's Rule: S_n = (h / 3) * [f(x_0) + 4 * Σ f(x_odd) + 2 * Σ f(x_even) + f(x_n)]
Theorems
Simpson's Rule
Trapezoidal Rule
Midpoint Rule
Suitable Grade Level
College Calculus or Advanced High School (Grades 11-12)
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