Let A be the area under the graph of an increasing continuousfunction f froma to b , and let Ln and Rn be the approximationsto A with n subintervals using left and rightendpoints, respectively.(a) How are A, Ln, and Rn related? (b) Give another estimate using the velocities at the end ofthe time periods.(c) Are your estimates in parts (a) and (b) upper and lowerestimates? Explain.
Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
Let A be the area under the graph of an increasing continuous
function f froma to b , and let Ln and Rn be the approximations
to A with n subintervals using left and right
endpoints, respectively.
(a) How are A, Ln, and Rn related?
(b) Give another estimate using the velocities at the end of
the time periods.
(c) Are your estimates in parts (a) and (b) upper and lower
estimates? Explain.
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