Speedometer readings for a vehicle (in motion) at 13-second intervals are given in the table. t (sec) v (ft/s) 28 13 21 26 24 39 19 52 26 65 18 Estimate the distance traveled by the vehicle during this 65-second period using the velocities at the beginning of the time intervals. We can do this by approximating the area under a curve. But what curve? In this case, imagine that the velocity of the vehicle is a function of time, v(t). We do not have this function, but we do have the values of the function at certain points in time. If we assume the function (the velocity) is constant between these points in time (which is not actually true), we can get an approximation. distance traveled = feet Give another estimate using the velocities at the end of the time periods. distance traveled & feet

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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.