Question

exercises 1.3 the fundamental theorem of calculus
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question 3
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using part i of the fundamental theorem of calculus, evaluate: \\(\frac{d}{dx} \int_{x}^{11} t^7 dt =\\)
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Explanation:

Step1: Reverse integral bounds

$\frac{d}{dx}\int_{x}^{11} t^7 dt = -\frac{d}{dx}\int_{11}^{x} t^7 dt$

Step2: Apply FTC Part 1

By the Fundamental Theorem of Calculus Part 1, $\frac{d}{dx}\int_{a}^{x} f(t)dt = f(x)$, so:
$-\frac{d}{dx}\int_{11}^{x} t^7 dt = -x^7$

Answer:

$-x^7$