Uploaded January 2026 | Updated September 2026, 3 weeks ago
In this video, we learn how to approximate the area under a curve using left and right endpoints (Riemann sums). We work through several examples step by step, using equal-width rectangles to estimate area and discussing when these methods produce overestimates or underestimates.
Topics covered:
📌 Using right endpoints to find Rn
📌 Using left endpoints to find Ln
📌 Approximating area under polynomial, trigonometric, and logarithmic functions
📌 Understanding overestimates vs. underestimates
This video is perfect for AP Calculus AB/BC, introductory calculus, or anyone learning how Riemann sums approximate area under curves.
Ready to try it yourself? Keep practicing Riemann Sums on IXL with interactive questions that adapt to your level: ixl.com/math/calculus/approximate-the-area-under-a-curve-left-and-right-endpoints?utm_source=youtube&utm_medium=social&utm_campaign=YT-Tutorials
0:00 Introduction
1:33 Find the area under the curve using right endpoints. f(x) = (-½)x^2+7
3:36 Find the area under the curve using left endpoints. f(x) = 3+ 2cos(x)
5:15 Find the area under the curve using left endpoints. f(x) = ln(6x)
6:48 Over vs. under estimates
In this video, we learn how to approximate the area under a curve using left and right endpoints (Riemann sums). We work through several examples step by step, using equal-width rectangles to estimate area and discussing when these methods produce overestimates or underestimates.
Topics covered:
📌 Using right endpoints to find Rn
📌 Using left endpoints to find Ln
📌 Approximating area under polynomial, trigonometric, and logarithmic functions
📌 Understanding overestimates vs. underestimates
This video is perfect for AP Calculus AB/BC, introductory calculus, or anyone learning how Riemann sums approximate area under curves.
Ready to try it yourself? Keep practicing Riemann Sums on IXL with interactive questions that adapt to your level: ixl.com/math/calculus/approximate-the-area-under-a-curve-left-and-right-endpoints?utm_source=youtube&utm_medium=social&utm_campaign=YT-Tutorials
0:00 Introduction
1:33 Find the area under the curve using right endpoints. f(x) = (-½)x^2+7
3:36 Find the area under the curve using left endpoints. f(x) = 3+ 2cos(x)
5:15 Find the area under the curve using left endpoints. f(x) = ln(6x)
6:48 Over vs. under estimates
