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A deposit has the grade attribute Xin[0,30]X in [0, 30]Xin[0,30] with a density function f(x)f(x)f(x). For a cut-off grade xcx_cxc, the proportion of the ore in the deposit is given by
∫030f(x)dx−∫0xcf(x)dx\int_{0}^{30} f(x) dx - \int_{0}^{x_c} f(x) dx∫030f(x)dx−∫0xcf(x)dx
12∫030f(x)dx−∫0xcf(x)dx\frac{1}{2} \int_{0}^{30} f(x) dx - \int_{0}^{x_c} f(x) dx21∫030f(x)dx−∫0xcf(x)dx
12∫030f(x)dx+∫0xcf(x)dx\frac{1}{2} \int_{0}^{30} f(x) dx + \int_{0}^{x_c} f(x) dx21∫030f(x)dx+∫0xcf(x)dx
∫0xcf(x)dx\int_{0}^{x_c} f(x) dx∫0xcf(x)dx
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