b. Compute the same integral the easy way (using the Fundamental Theorem Calculus). Make sure you get the same answer.
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However, the specific integral is not provided in the text. To proceed, I will assume a generic integral of the form \(\int_a^b f(x) \, dx\) and demonstrate how to compute it using the Fundamental Theorem of Calculus. ### Show more…
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(a) Make an appropriate u-substitution, and then use the Endpaper Integral Table to evaluate the integral. (b) If you have a CAS, use it to evaluate the integral (no substitution), and then confirm that the result is equivalent to that in part (a). $$\int \cos \sqrt{x} d x$$
PRINCIPLES OF INTEGRAL EVALUATION
Using Computer Algebra Systems and Tables of Integrals
(a) Use the Endpaper Integral Table to evaluate the given integral. (b) If you have a CAS, use it to evaluate the integral, and then confirm that the result is equivalent to the one that you found in part (a). $$\int \frac{1}{x^{2} \sqrt{x^{2}-2}} d x$$
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