Chapter 4: Q. 1 (page 327)
Use the graph of f to estimate the values of A(1), A(2), A(3)
The area of A(1) is zero
The area of A(2) is 2.5 sq. units
The area of A(3) is 8.5 sq. units
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Verify that. (Do not try to solve the integral from scratch.)
For each function f and interval [a, b] in Exercises 27–33, use the given approximation method to approximate the signed area between the graph of f and the x-axis on [a, b]. Determine whether each of your approximations is likely to be an over-approximation or an under-approximation of the actual area.
left sum with
a) n = 3 b) n = 6
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Show that is an antiderivative of .
Show by exhibiting a counterexample that, in general, . In other words, find two functions f and g such that the integral of their quotient is not equal to the quotient of their integrals.
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