Question

homework 1: 1.1-1.4 review
score: 10/17 answered: 7/13
question 8
using part i of the fundamental theorem of calculus, evaluate \\(\frac{d}{dx}\int_{16}^{x} t^3 dt\\).
\\(\frac{d}{dx}\int_{16}^{x} t^3 dt = \\)

Explanation:

Step1: Recall Fundamental Theorem of Calculus Part I

For a continuous function $f(t)$ on an interval containing $a$ and $x$, $\frac{d}{dx}\int_{a}^{x} f(t)dt = f(x)$.

Step2: Identify $f(t)$ in the integral

Here, $f(t) = t^3$, $a=16$.

Step3: Apply the theorem

Substitute $t$ with $x$ in $f(t)$.

Answer:

$x^3$