Question

question 9 · 1 point given f(x) below, find f(x). f(x)=\int_{3}^{x}-\frac{3}{2t + 7}dt provide your answer below: f(x)=□

Explanation:

Step1: Apply the fundamental theorem of calculus

If $F(x)=\int_{a}^{x}f(t)dt$, then $F^{\prime}(x)=f(x)$. Here, $a = 3$ and $f(t)=-\frac{3}{2t + 7}$.

Step2: Find the derivative of $F(x)$

Substitute $t=x$ into $f(t)$. So $F^{\prime}(x)=-\frac{3}{2x+7}$.

Answer:

$-\frac{3}{2x + 7}$