The table gives the values of a function obtained from an experiment. Use the table to estimate f(x) dx using three equal subintervals and a right Riemann sum, left Riemann sur sum. 3 4 5 6 7 8 9 f(x) -3.3 -2.2 -0.7 0.3 0.7 1.5 1.9 (a) Estimate f(x) dx using three equal subintervals and right endpoints. R3 = 2.85 If the function is known to be an increasing funtion, can you say whether your estimate is less than or greater than the exact value of the integral? less than O greater than one cannot say (b) Estimate f(x) dx using three equal subintervals and left endpoints. L3 = If the function is known to be an increasing funtion, can you say whether your estimate is less than or greater than the exact value of the integral? O less than greater than one cannot say (c) Estimate f(x) dx using three equal subintervals and midpoints.

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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.