Evaluate the Integral

Problem

(∫_1^8)(1/x*d(x))

Solution

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

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

[ln(x)]81

3. Substitute the upper limit 8 and the lower limit 1 into the expression.

ln(8)−ln(1)

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

ln(8)−0

5. Rewrite the result if necessary. Since 8=2 the expression can also be written as 3*ln(2) though ln(8) is a standard form.

ln(8)

Final Answer

(∫_1^8)(1/x*d(x))=ln(8)

Want more problems? Check here!