Find the area of the region bounded by the curve y = ln(x)/x, the x-axis, and the line x = e.

Vault Of Euclid

Area Under the Curve of ln(x)/x

Techniques of integration warmup

Let \( \mathcal{R} \) be the region bounded by the curve \( y = \frac{\ln x}{x} \), the \( x \)-axis, and the line \( x = e \). Find the area of \( \mathcal{R} \).

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What you need first

Finding the roots of a logarithmic function
Setting up a definite integral for the area under a curve
Integration by substitution (u-substitution)
Evaluating definite integrals using the Fundamental Theorem of Calculus
Values of the natural logarithm at 1 and e

What this problem tests

Tests setting up an area integral by finding the intersection with the x-axis, and evaluating the integral using u-substitution.

This is a standard Calculus I problem that tests the ability to set up an area integral and evaluate it using u-substitution.

Area Under the Curve of ln(x)/x

What you need first

What this problem tests

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