Integral, why antiderivative is area under curve

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SUMMARY

The integral, specifically the antiderivative, represents the area under a curve defined by a function f(x). The relationship is established through the Fundamental Theorem of Calculus, which states that if F is an antiderivative of f on an interval [A, B], then the integral from A to B of f(x) dx equals F(B) - F(A). The discussion highlights the equation f'(c) * Δx = Δy, emphasizing that the area can be approximated as Δx * f(c) for small intervals, reinforcing the connection between derivatives and integrals.

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  • Understanding of the Fundamental Theorem of Calculus
  • Knowledge of derivatives and antiderivatives
  • Familiarity with the concept of limits in calculus
  • Basic proficiency in mathematical notation and functions
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  • Study the Fundamental Theorem of Calculus in detail
  • Explore Riemann sums and their relation to integrals
  • Learn about the Mean Value Theorem for integrals
  • Investigate applications of integrals in real-world scenarios
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Students of calculus, educators teaching integral calculus, and anyone seeking a deeper understanding of the relationship between derivatives and the area under curves.

kidsasd987
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well, no it makes sense. sorry. I will delete this thread
 

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