a) Integrate ln(x) + 1/x - x to find the equation for Curve A b) find the x coordinate on Curve A when y = 0.
a) Integrate ln(x) by parts: u = ln(x), dv/dx = 1, du/dx = 1/x, v = x int(udv/dx) = uv - int(du/dx * v) = ln(x)/x - x so int(ln(x) + 1/x - x) = ln(x)/x - x + ln(x) + x^2 + Cb) y = ln(x)/x - x + ln(x) + x^2 = 0 By logic, x will always be positive and through judgement/trial and error, x =1 OR, can rearrange: x = sqrt(x - ln(x)(1 + 1/x)) and carry out iterations until x=1 is found.
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