Question:medium
If \( \int \frac{1}{2x^2} \, dx = k \cdot 2x + C \), then \( k \) is equal to:
If \( \int \frac{1}{2x^2} \, dx = k \cdot 2x + C \), then \( k \) is equal to:
Show Hint
For integrals involving powers of \( x \), use the power rule: \( \int x^n \, dx = \frac{x^{n+1}}{n+1} + C \).
Updated On: Mar 8, 2026
- \( -1 \)
- \( \log 2 \)
- \( -\log 2 \)
- \( 1/2 \)
Show Solution
The Correct Option is D
Solution and Explanation
The integral of \( \frac{1}{2x^2} \) is \( \int \frac{1}{2x^2} \, dx = -\frac{1}{2x} + C \). Comparing this to \( k \cdot 2x + C \), we determine \( k = \frac{1}{2} \).
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