$\int_{0}^{4}\left(\sqrt{x}+\dfrac{1}{\sqrt{x}}\right)dx$ is : (a) $\dfrac{28}{3}$ (b) $\dfrac{20}{3}$ (c) $\dfrac{1}{3}$ (d) $\dfrac{21}{3}$

∫₀⁴(√(x)+dfrac1√(x))dx is : (a) (28)/(3) (b) (20)/(3) (c) (1)/(3) (d) (21)/(3)

Question 35 of 42

\int_{0}^{4}\left(\sqrt{x}+\dfrac{1}{\sqrt{x}}\right)dx

(a)

\dfrac{28}{3}

(b)

\dfrac{20}{3}

(c)

\dfrac{1}{3}

(d)

\dfrac{21}{3}

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Integrate $x^{1/2}$ and $x^{-1/2}$ by the power rule, then evaluate from $0$ to $4$ to get $\dfrac{28}{3}$ , option (a).

Antiderivative.

$\int\Big(x^{1/2}+x^{-1/2}\Big)dx=\frac{x^{3/2}}{3/2}+\frac{x^{1/2}}{1/2}=\frac{2}{3}x^{3/2}+2\sqrt{x}.$

Apply the limits. …