Question

The value of \( \int_{0}^{1} \frac{dx}{1 + x^{2}} \) is:

• A. $\pi/4$
• B. $\pi/2$
• C. 1
• D. 0

Hint:

$\tan^{-1}(1) = \pi/4$ is one of the most frequently used values in calculus.

Answer 1

The Correct Option is A

Step 1: Concept
The standard integral is $\int \frac{1}{1+x^2} dx = \tan^{-1} x + c$.
Step 2: Analysis
Applying limits: $[\tan^{-1} x]_{0}^{1} = \tan^{-1}(1) - \tan^{-1}(0)$.
Step 3: Conclusion
$= \pi/4 - 0 = \pi/4$.
Final Answer: (A)