Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.6 Logarithmic And Other Functions Defined By Integrals - Exercises Set 6.6 - Page 460: 20

$\bf{True}$

For $a \gt0$, we have: $\int_{1}^{\sqrt a} \dfrac{1}{t} \ dt=[\ln t]_{1}^{\sqrt a}=[\dfrac{\ln (a)}{2}-0]=\dfrac{\ln (a)}{2}$ Also, $\dfrac{1}{2} \int_{1}^{a} \dfrac{1}{t} \ dt=\dfrac{1}{2}[\ln t]_{1}^{a}=\dfrac{1}{2} [\ln (a)-0]=\dfrac{\ln (a)}{2}$ Hence, the given statement is $\bf{True}$.