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in Integrals calculus by (41.4k points)

Compute the area of the region bounded by the curves y = ex In x, and y = (lnx/ex).

1 Answer

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Best answer

See Fig.

Given curves are

y = exlnx    (1)

y = lnx/ex    (2)

Points of intersection of (1) and (2) are P(1/e, - 1) and Q(1, 0)

For curve (1), y < 0 for 0 < x < 1 and y ≥ 0 for x ≥ 1

Obviously y → 0 when x → 0 

For curve (2), y → -∞ when x → 0 

y < 0 for 0 < x < 1, y ≥ 0 for x ≥ 1 

Obviously y → 0 when x → ∞ 

This shape of curves is depicted in Figure

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