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Chapter 4: Q. 17 (page 362)
Show by exhibiting a counterexample that, in general, . In other words, find two functions f and g so that the integral of their product is not equal to the product of their integrals.
The counterexample is
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What is the difference between an antiderivative of a function and the indefinite integral of a function?
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Without using absolute values, how many definite integrals would we need in order to calculate the absolute area between f(x) = sin x and the x-axis on ?
Will the absolute area be positive or negative, and why? Will the signed area will be positive or negative, and why?
Verify that(Do not try to solve the integral from scratch.
For each function f and interval [a, b] in Exercises 27鈥�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.
, n = 3 with
a) Trapezoid sim b) Upper sum
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