The rate of change of profit for a company is given by p(t) = 357 e-0.18t thousand dollars per year, t years since 2000, Os ts 8. Check: p(2)=249.070448407358 p(t) thousand dollars per year 350p 300 250 200 150 100 50 t years since 2000 0 1 2 3 45 6 7 8 We wish to estimate the area trapped between p(t) and the t -axis from t = 0 to t = 8 using two midpoint rectangles of equal width. (a) Complete the sigma notation for the area estimation described above by providing the width of each rectangle and the input values used to calculate the height of each rectangle. Area - p(t;)At = Ac i = 1 where At = t2 = (b) Complete the calculation for the rectangle area estimation described above. Round your answer to 3 decimal places.

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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.