Our mission is to provide a free, world-class education to anyone, anywhere.

Learn how to approximate the area under a curve using the trapezoidal rule on Khan Academy.

Riemann sums is the name of a family of methods we can use to approximate the area under a curve. Through Riemann sums we come up with a formal definition for the definite integral.

Help us do more We'll get right to the point: we're asking you to help support Khan Academy. We're a nonprofit that relies on support from people like you. If everyone reading this gives …

Analyze Riemann sums of various functions to determine if they are an over-estimation or an under-estimation of the actual area.

We took the average of the two heights and multiplied that times the base. Now, if we wanted the sum of the areas of all these trapezoids, and we wanted to write in general terms, we could …

ವೀಡಿಯೊ ಪ್ರತಿಲಿಪಿ - [Tutor] Imagine we're asked to approximate the area between the x-axis and the graph of f from x equals one to x equals 10 using a right Riemann sum with …

The area under a curve is commonly approximated using rectangles (e.g. left, right, and midpoint Riemann sums), but it can also be approximated by trapezoids. Trapezoidal sums actually …

And it's a left Riemann sum, so we would use the value of the function at the left end of that subdivision, which is negative seven, x equals negative seven. The value of the function there …

To do that, we are given a table of values for f, so I encourage you to pause the video and see if you can come up with an approximation for the area between the x axis and the graph from x …