Calculus › Section E · Integrals › Topic E.1
Antiderivatives and indefinite integrals
Every derivative fact can be run backwards: if a curve's slope is known, the curve can be rebuilt up to a vertical shift. Antiderivatives are that reversal, and they are the doorway into integral calculus.
In this topic
- Running the machine backwards
- Antiderivatives and the +C family
- Indefinite integral notation
- The reverse power rule
- Worked example: a polynomial, with the check
- The trig and exponential staples
- Worked example: pinning down one curve
- Worked example: rebuilding motion
- Where the constants come from
- Common mistakes to avoid
- Key takeaways
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Standards: 6