Question

Evaluate: $\int x \, dx$

• A. $x$
• B. $\frac{x^2}{2} + C$
• C. $\ln x$
• D. $x^2 + C$

Hint:

Never forget to add the constant of integration ($+ C$) for indefinite integrals! It represents any constant that might have disappeared during differentiation.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Integration is the reverse process of differentiation. For a power function $x^n$, the power rule for integration is: $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$ (where $n \neq -1$).
Step 2: Detailed Explanation:
In this question, $x$ can be written as $x^1$. Applying the rule:
$$\int x^1 \, dx = \frac{x^{1+1}}{1+1} + C = \frac{x^2}{2} + C$$
Step 3: Final Answer:
The correct option is (b).