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## Integral Calculus

### Unit 3: Lesson 7

Volume: squares and rectangles cross sections

# Volumes with cross sections: squares and rectangles (intro)

AP.CALC: CHA‑5 (EU), CHA‑5.B (LO), CHA‑5.B.1 (EK)

## Problem

Let f, left parenthesis, x, right parenthesis, equals, 5, minus, x and g, left parenthesis, x, right parenthesis, equals, 2, dot, start text, s, i, n, end text, left parenthesis, start fraction, pi, x, divided by, 6, end fraction, right parenthesis. Let R be the region enclosed by the graphs of f and g and the y-axis.
Region R is the base of a solid. For each x-value, the cross section of the solid taken perpendicular to the x-axis is a rectangle whose base lies in R and whose height is 2, x.
Which one of the definite integrals gives the volume of the solid?