Question

\(3\displaystyle \int \sqrt{x}\,dx=\) ?

• A. \(\dfrac{9}{2}x^{3/2}+k\)
• B. \(2x^{3/2}+k\)
• C. \(3x^{3/2}+k\)
• D. \(\dfrac{2}{3}x^{3/2}+k\)

Hint:

Power rule: $\int x^{n}dx=\dfrac{x^{n+1}}{n+1}+C$ for $n\neq -1$.

Answer 1

The Correct Option is B

\(\int x^{1/2}dx=\dfrac{x^{3/2}}{3/2}=\dfrac{2}{3}x^{3/2}\). Multiply by \(3\): \(3\cdot\dfrac{2}{3}x^{3/2}=2x^{3/2}+k\).