Question

question. given that $f(x)=int_{0}^{x}sqrt{5 + ln{3t}}dt$, what is $f(x)$? (do not include \$f(x)=$\ in your answer.) provide your answer below.

Explanation:

Step1: Apply fundamental theorem of calculus

The fundamental theorem of calculus states that if $F(x)=\int_{a}^{x}f(t)dt$, then $F^{\prime}(x) = f(x)$. Here, $a = 0$ and $f(t)=\sqrt{5+\ln3t}$.

Step2: Find the derivative

By the fundamental theorem of calculus, when differentiating $F(x)=\int_{0}^{x}\sqrt{5 + \ln3t}dt$ with respect to $x$, we get $F^{\prime}(x)=\sqrt{5+\ln3x}$.

Answer:

$\sqrt{5+\ln3x}$