📈Derivative vs Integral∫
Calculus has two central operations that are deeply linked. One zooms in on instantaneous change; the other sums up small pieces.
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📈Derivative
- ✓Measures the instantaneous rate of change
- ✓Gives the slope of a curve at a point
- ✓Found by differentiation
- ✓Velocity is the derivative of position
- ✓Used to find maximum and minimum values
∫Integral
- ✓Measures total accumulation over an interval
- ✓Gives the area under a curve
- ✓Found by integration
- ✓Distance is the integral of velocity
- ✓Used to compute areas, volumes and totals
Verdict
Derivatives and integrals are inverse operations, joined by the Fundamental Theorem of Calculus. Differentiating undoes integrating, and vice versa. Together they describe both change and accumulation.
Frequently asked
How are derivatives and integrals related?+
They are inverse operations, linked by the Fundamental Theorem of Calculus.
What does a derivative tell you?+
It gives the rate of change at an instant — for example, the slope of a curve at one point.
What does an integral compute?+
It computes accumulated quantities, most commonly the area under a curve over an interval.
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