Evaluate the Integral

Problem

(∫_1^e)(1/x*d(x))

Solution

1. Identify the antiderivative of the function 1/x The antiderivative of 1/x is ln(x)

2. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper limit e and the lower limit 1

3. Substitute the limits into the expression ln(x)

[ln(x)]e1

4. Calculate the difference between the values at the boundaries.

ln(e)−ln(1)

5. Simplify the logarithmic values. Since ln(e)=1 and ln(1)=0 the result is 1 - 0$.

1−0=1

Final Answer

(∫_1^e)(1/x*d(x))=1

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