Isaac claims that since he knows how to use the Fundamental Theorem of Calculus to find...

 

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Isaac claims that since he knows how to use the Fundamental Theorem of Calculus to find the integral of functions he does not need to know how to take a Riemann sum. (a) Provide an example of a function where the antiderivative is not possible, or at least extremely difficult, to calculate to show that the FTC is not always efficient. (b) For that function and an appropriate subinterval of its domain, find the right Riemann sum and the left Riemann sum for n = 8, then estimate the area of the function on the subinterval. Isaac claims that since he knows how to use the Fundamental Theorem of Calculus to find the integral of functions he does not need to know how to take a Riemann sum. (a) Provide an example of a function where the antiderivative is not possible, or at least extremely difficult, to calculate to show that the FTC is not always efficient. (b) For that function and an appropriate subinterval of its domain, find the right Riemann sum and the left Riemann sum for n = 8, then estimate the area of the function on the subinterval.

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