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The area enclosed between the curves y =loge (x + e), x = logeand the x-axis is
y =loge (x + e) and x = loge look like –
The curves intersect at (0, 1)
(Putting x = 0 in the 2 curves, y = loge(e) = 1 and 0 = loge(1/y),
i.e., y = 1/e0 = 1)
So, bounds are x = 1 – e to x = 0 for the first curve and then x = 0 to apparently x = ∞ for the second curve.