Math Problem Statement
Evaluate the integral
x sin(xy) 81 + z2 dV
E where E =
(x,y,z)| 1 ≤ x ≤ 2, 0 ≤ y ≤ 3𝜋, 0 ≤ z ≤ 9
.
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Triple Integrals
Trigonometric Integrals
Integration by Parts
Formulas
Triple Integral: ∫∫∫ f(x, y, z) dV
Integration by Parts: ∫ u dv = uv - ∫ v du
Standard Integral: ∫ 1/(a^2 + z^2) dz = (1/a) * arctan(z/a)
Theorems
Fubini's Theorem
Integration by Parts
Arctangent Integral
Suitable Grade Level
College Level
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