Study notes
Integration
Integration as the reverse of differentiation for polynomials, always with '+C' on indefinite integrals, definite integrals, area under a curve, and simple kinematics.
What this topic covers
- Integration reverses the power rule: raise the power by one, then divide by the NEW power
- An indefinite integral must ALWAYS end in '+C'; forgetting it is a real, common error
- A constant on its own integrates to (constant) \(\times\, x\), plus C
- A definite integral has limits and gives a NUMBER, with no '+C'
- The area under a curve, above the x-axis, between two x-values is a definite integral
- Kinematics: displacement, velocity, and acceleration are linked by differentiation and integration in opposite directions
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