Math Problem Statement

  1. Evaluate the following iterated integrals (a) Z 3 0 Z π/2 0 x2 sin(y) dydx (b) Z 5 3 Z 5 0 dydx x + y (c) Z Z D 23x y dA, where D = [−2, 4] × [1, 3].

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Double Integrals
Iterated Integrals
Integration Techniques

Formulas

Double integral formula ∫∫_D f(x, y) dA
Integration of trigonometric functions ∫ sin(y) dy = -cos(y)
Logarithmic integration ∫ 1/(x + y) dy = ln(x + y)

Theorems

Fubini's Theorem for double integrals

Suitable Grade Level

Undergraduate Calculus