Which of the following approximations to integration would give exact results? 1) Left-handed Riemann sum on a linear function 2) Left-handed Riemann sum on an increasing function 3) Midpoint Riemann sum on a linear function 4) Right-handed Riemann sum on a decreasing function
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.
Which of the following approximations to
1) Left-handed Riemann sum on a linear function
2) Left-handed Riemann sum on an increasing function
3) Midpoint Riemann sum on a linear function
4) Right-handed Riemann sum on a decreasing function
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