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Riemann Sums - Left Endpoints and Right Endpoints
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This calculus video tutorial provides a basic introduction into riemann sums. It explains how to approximate the area under the curve using rectangles over a closed interval. It explains how to determine the area of the region using left endpoints and right endpoints. The area under the curve is also equal to the definite integral of the function over the closed interval. The area can be approximated by taking the sum of the area of each rectangle. You can express this using sigma notation and calculate the sum using the appropriate summation formulas. The area of each rectangle is simply the product of the width and the height. The width is delta x and it represents the length of each subinterval. The height of the rectangle is represented by y which is a function of x or simply f(x). The average of the areas using the left and right endpoints is very close to the actual area under the curve. This tutorial contains a few examples and practice problems. The area using left endpoints is an under approximation or lower sum and the area using right endpoints is an over approximation or upper sum when the function is increasing. The upper sum is the higher of the two values and the lower sum is the lower of the two values.
Antiderivatives:
Basic Integration Problems:
Indefinite Integral:
Definite Integral:
Differential Equations:
_______________________________
Properties of Definite Integrals:
Rectilinear Motion Problems:
Sigma Notation - Calculus:
Riemann Sums - Area:
The Midpoint Rule:
________________________________
Finding Area - Limit Definition:
Definite Integrals - Geometry:
Fundamental Theorem - Part 1:
Fundamental Theorem - Part 2:
Net Change Theorem:
__________________________________
Final Exams and Video Playlists:
Full-Length Videos and Worksheets:
Antiderivatives:
Basic Integration Problems:
Indefinite Integral:
Definite Integral:
Differential Equations:
_______________________________
Properties of Definite Integrals:
Rectilinear Motion Problems:
Sigma Notation - Calculus:
Riemann Sums - Area:
The Midpoint Rule:
________________________________
Finding Area - Limit Definition:
Definite Integrals - Geometry:
Fundamental Theorem - Part 1:
Fundamental Theorem - Part 2:
Net Change Theorem:
__________________________________
Final Exams and Video Playlists:
Full-Length Videos and Worksheets:
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