Describe, in one or two sentences, why the definite integral ( _ a ^ b h(x) ,w(x) ,dx…

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Describe, in one or two sentences, why the definite integral ∫abh(x) w(x) dx\displaystyle \int_{a}^{b} h(x)\,w(x)\,dx represents the exact volume of a solid whose cross sections perpendicular to the xx-axis are rectangles with height h(x)h(x) and base width w(x)w(x) on the interval [a,b][a,b].

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