Evaluate the Integral

Problem

(∫_1^4)(1/x*d(x))

Solution

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

2. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper and lower limits of integration.

(∫_1^4)(1/x*d(x))=[ln(x)]41

3. Substitute the limits into the expression.

ln(4)−ln(1)

4. Simplify the expression using the fact that ln(1)=0

ln(4)−0

5. Rewrite the result if necessary. Since 4=2 the answer can also be expressed using logarithm properties as 2*ln(2)

Final Answer

(∫_1^4)(1/x*d(x))=ln(4)

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