Practice question · Fill in the blanks
Complete the statement of the first part of the theorem.
If F(x) is defined as the integral of f from a fixed a up to x, then F'(x) equals ______.
Word bank: f(x) · F(x) · f'(x) · the area under f
Hints
- Ask what the accumulation function is accumulating at the moment x.
- The rate at which area piles up is governed by how tall the curve is right there.
Show the answer
If F(x) is defined as the integral of f from a fixed a up to x, then F'(x) equals f(x).
Why
The derivative of the accumulated area is the height of the curve, f(x). This is the statement that differentiation undoes integration, and it is why velocity integrates to displacement and a rate integrates to a total.
Practise The Fundamental Theorem of Calculus
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