Question

exercises 1.3 the fundamental theorem of calculus
score: 60/260 answered: 6/26
question 7
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use part i of the fundamental theorem of calculus to find the derivative of
$f(x)=int_{-2}^{x} sqrt{t^{3}+2^{3}}dt$
$f(x) = $
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Explanation:

Step1: Recall Fundamental Theorem of Calculus Part 1

For a function $f(x) = \int_{a}^{x} g(t)dt$, where $a$ is a constant, $f'(x) = g(x)$.

Step2: Identify $g(t)$ in the given integral

Here, $g(t) = \sqrt{t^3 + 2^3} = \sqrt{t^3 + 8}$.

Step3: Substitute $x$ for $t$ in $g(t)$

Replace $t$ with $x$ in $g(t)$ to get $f'(x)$.

Answer:

$\sqrt{x^3 + 8}$