Subject GRE-Style: Setting Up Multiple Integrals

GRE Math Subject · Axiom Academy

EXAMPLE GRE-Style Setting Up Multiple Integrals The region R is bounded by the curves y = x and y = x^2 . First, find their intersection points: So the curves intersect at x = 0 and x = 1 . For 0 0 ). For a fixed , y ranges from y = x^2 (lower bound) to y = x (upper bound). Thus we integrate with respect to y first: The inner integral integrates z = x + y over the vertical line segment from height x^2 to x at fixed x . The outer integral sums over all x from 0 to 1. This is correct! GRE Insight: Setting up integrals correctly requires careful region analysis. Sketch if possible, identify intersection points, and determine which variable's bounds depend on the other.

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