Pollution from a factory is entering a lake. The rate of concentration of the pollutant at time t is given by P ' ( t ) = 90 t 1/2 , where t is the number of years since the factory started introducing pollutants into the lake. Ecologists estimate that the lake can accept a level of pollution of 4850 units before all fish life in the lake ends. a. Set up the definite integral that gives the total pollutant concentration in the lake after 4 years. b. Can the factory operate for 5 years without killing all the fish in the lake?
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.
Pollution from a factory is entering a lake. The rate of concentration of the pollutant at time t is given by P ' ( t ) = 90 t 1/2 , where t is the number of years since the factory started introducing pollutants into the lake. Ecologists estimate that the lake can accept a level of pollution of 4850 units before all fish life in the lake ends.
a. Set up the definite
b. Can the factory operate for 5 years without killing all the fish in the lake?
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