Question:
\(3\displaystyle \int \sqrt{x}\,dx=\) ?
\(3\displaystyle \int \sqrt{x}\,dx=\) ?
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Power rule: $\int x^{n}dx=\dfrac{x^{n+1}}{n+1}+C$ for $n\neq -1$.
Updated On: Oct 17, 2025
- \(\dfrac{9}{2}x^{3/2}+k\)
- \(2x^{3/2}+k\)
- \(3x^{3/2}+k\)
- \(\dfrac{2}{3}x^{3/2}+k\)
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The Correct Option is B
Solution and Explanation
\(\int x^{1/2}dx=\dfrac{x^{3/2}}{3/2}=\dfrac{2}{3}x^{3/2}\).
Multiply by \(3\): \(3\cdot\dfrac{2}{3}x^{3/2}=2x^{3/2}+k\).
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