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Chapter 4: Q. 33 (page 404)
Integral Formulas:
Fill in the blanks to complete each of the following integration formulas.
(The last six formulas involve hyperbolic functions and their inverses.)
Ans:
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Determine which of the limit of sums in Exercises 47–52 are infinite and which are finite. For each limit of sums that is finite, compute its value
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
If f is negative on [−3, 2], is the definite integral positive or negative? What about the definite integral − ?
Without using absolute values, how many definite integrals would we need in order to calculate the area between the graphs of f(x) = sin x and g(x) = on ?
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.
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