Evaluate the Integral

Problem

(∫_0^ln(2))(ex*d(x))

Solution

1. Identify the integral as a definite integral of the exponential function ex

2. Find the antiderivative of ex which is simply ex

3. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper limit ln(2) and the lower limit 0

[ex]ln(2)0

4. Substitute the limits into the expression.

eln(2)−e0

5. Simplify the terms using the properties of logarithms and exponents, noting that eln(2)=2 and e0=1

2−1

6. Calculate the final difference.

1

Final Answer

(∫_0^ln(2))(ex*d(x))=1

Want more problems? Check here!