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Chapter 4: Q. 60 (page 327)
Given a simple proof that if n is a positive integer and c is any real number, then
We proved
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Prove Theorem 4.13(b): For any real numbers a and b, we have. Use the proof of Theorem 4.13(a) as a guide.
Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating .
Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: ).
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Explain why the formula for the integral of does not
apply when What is the integral of
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