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Today's calculation of Integral 580

Source: 2010 Hiroshima University entrance exam/Humanities

March 11, 2010
calculusintegrationanalytic geometrygeometrycalculus computations

Problem Statement

Let k k be a positive constant number. Denote α, β (0<β<α) \alpha ,\ \beta \ (0<\beta <\alpha) the x x coordinates of the curve C: y\equal{}kx^2\ (x\geq 0) and two lines l: y\equal{}kx\plus{}\frac{1}{k},\ m: y\equal{}\minus{}kx\plus{}\frac{1}{k}.　Find the minimum area of the part bounded by the curve C C and two lines l, m l,\ m.
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