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2. For each the following types of functions, a "shortcut" exists for calculating the integrals. In this problem, you will discover the "shortcut", and see why it works. Start by using the Substitution Method to evaluate the indefinite integrals in (a) - (f) (a) cos(4)dr (b)sin(7x)dr c4sin(-3r)dx (e) /5e2dx dx 4x-3 (g) What is happening in each of these problems? That is, what is the common aspect of each of the antiderivatives? (This is the "shortcut" that you should be observing.) (h) What do each of the differentials in these problems have in common? (Note: This is not just a coincidence. This is the entire reason that the "shortcut" works. It wil not work for other types of problems!)
2. For each the following types of functions, a "shortcut" exists for calculating the integrals. In this problem, you will discover the "shortcut", and see why it works. Start by using the Substitution Method to evaluate the indefinite integrals in (a) - (f) (a) cos(4)dr (b)sin(7x)dr c4sin(-3r)dx (e) /5e2dx dx 4x-3 (g) What is happening in each of these problems? That is, what is the common aspect of each of the antiderivatives? (This is the "shortcut" that you should be observing.) (h) What do each of the differentials in these problems have in common? (Note: This is not just a coincidence. This is the entire reason that the "shortcut" works. It wil not work for other types of problems!)
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Patrina SchowalterLv2
13 Nov 2019