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Triple integrals

Multivariable and vector calculus · Mathematics

Study notes

Q: Evaluate the integral from 0 to 1 of the integral from 0 to 1 of the integral from 0 to 1 of (x + y + z) dz dy dx. Innermost (z): [xz + yz + z^2/2] 0 to 1 = x + y + 1/2. Middle (y): integral 0 to 1 of (x + y + 1/2) dy = [xy + y^2/2 + y/2] 0 to 1 = x + 1. Outer (x): integral 0 to 1 of (x+1) dx = 3/2.

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