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.
Complete the following steps for the given integral and the given value of n.
a. Sketch the graph of the integrand on the interval of
b. Calculate ∆x and the grid points x0, x1,........., xn, assuming a regular
partition.
c. Calculate the left and right Riemann sums for the given value of n.
d. Determine which Riemann sum (left or right) underestimates the
value of the definite integral and which overestimates the value of
the definite integral.
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