Step {{ Math.min(currentStep, totalSteps) }} of {{ totalSteps }}
Fill the Area
How can we measure the area under this curve? Let's approximate it with shapes we know.
TAP TO PLACE RECTANGLES
Great! We formed a Left Riemann Sum.
Endpoint Matters
Where the rectangle touches the curve changes the estimation.
DRAG LABELS TO MATCH GRAPHS
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Drop here
The Power of
As we use more rectangles (increase ), what happens to the approximation?
SLIDE TO REFINE APPROXIMATION
Error
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Limit Reached!
Target: < 0.1
A Better Shape
Rectangles are blocky. Let's adjust the tops to match the curve.
DRAG HANDLES TO CURVE
Trapezoidal Rule applied! Much closer fit.
Master of Approximation!
You've explored how rectangles and trapezoids can estimate area, and how the limit as gives us the Definite Integral.