The value of \(\int_{1}^{4}\displaystyle \sqrt{x}\,dx\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{14}{3}\)
Writing \(\sqrt{x} = x^{\frac{1}{2}}\) and using the power rule:
\( \displaystyle \int_{1}^{4}x^{\frac{1}{2}}\,dx = \Big[\frac{2}{3}x^{\frac{3}{2}}\Big]_{1}^{4} \)
\( \displaystyle = \frac{2}{3}(8 - 1) \)
\( \displaystyle = \frac{14}{3} \)