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Fundamental Theorem of Calculus

The New York Times · 12 min read

Fundamental Theorem of Calculus

The solution to the differential equation can be expressed as:

\int_{a}^{b} f(x) \, dx = F(b) - F(a)

Where

F(x)

is the antiderivative of

f(x)

. This fundamental theorem connects differentiation and integration.

We can further show that for any continuous function

g(t)

, the accumulation function

A(x) = \int_{a}^{x} g(t) \, dt

is differentiable.

AI LearnEN

Explain this section logic.

The author explains the Fundamental Theorem of Calculus.

It links the concept of the derivative (rate of change) with the integral (accumulation), showing they are inverse processes.

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How Reedle compares for research reading

	Reedle	ChatPDF	NotebookLM
Price	$4.99/mo (30-day trial)	$20/mo	Free (Google account)
Mobile LaTeX rendering	Yes	No	No
Zotero integration	Bulk import	No	No
Full-text AI chat	Yes	Yes	Yes
Cross-paper RAG	Yes (library search)	No	Limited
Spaced repetition	FSRS built-in	No	No
Highlighting + notes	Yes	Basic	Limited
Offline reading	Yes (PWA)	No	No
Data export	Full export	No	No

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