Math Problem Statement

By reversing the order of integration, evaluate the integral
∫ 6 0 ∫ 2 y 3 y cos ( x 3 − 6 ) d x d y .

Solution

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Math Problem Analysis

Mathematical Concepts

Double Integrals
Order of Integration
Trigonometric Functions
Substitution Method

Formulas

Double integral formula: ∫∫ f(x,y) dx dy
Substitution: u = x^3 - 6

Theorems

Fubini's Theorem for reversing the order of integration

Suitable Grade Level

College-level Calculus