Question

$\int_{-\log 3}^{+\log 3} e^{|x|} dx = $ ________.

• A. 3
• B. 6
• C. 4
• D. 8
• E. 0

Hint:

$e^{\log a} = a$.

Answer 1

The Correct Option is C

Step 1: Concept
$e^{|x|}$ is an even function, so $\int_{-a}^{a} f(x) dx = 2\int_{0}^{a} f(x) dx$.

Step 2: Meaning
The integral becomes $2 \int_{0}^{\log 3} e^x dx$.

Step 3: Analysis
$2 [e^x]_0^{\log 3} = 2 (e^{\log 3} - e^0) = 2 (3 - 1)$.

Step 4: Conclusion
$2 \times 2 = 4$. Final Answer: (C)