Question

exercises 1.3 the fundamental theorem of calculus
score: 30/260 answered: 3/26
question 4
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use part i of the fundamental theorem of calculus to find each of the following when $f(x)=\int_{1}^{x} t^{5} dt$.
$f(x) = $
$f(-5) = $
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Explanation:

Step1: Apply Fundamental Theorem of Calculus Part I

For $f(x)=\int_{a}^{x} g(t)dt$, $f'(x)=g(x)$. Here $g(t)=t^5$, so:
$f'(x)=x^5$

Step2: Evaluate derivative at $x=-5$

Substitute $x=-5$ into $f'(x)$:
$f'(-5)=(-5)^5$

Answer:

$f'(x)=x^5$
$f'(-5)=-3125$