The self-tests are here: answers and some links are below the fold. Please also check Piazza where students may have posted solutions and I may have commented or approved!

MAT1575Test1Review

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Please let me know (by email or on Piazza)  if you find any typographical or other errors in these!

Answers and hints to Self-Test 1:

• 1)
• 2) : use substitution
• 3) : integrate by parts twice (Note: corrected sign for next-to-last term)
• 4) : integrate by parts
• 5) : use substitution
• 6) : FTC part II (no work to show, just state the FTC part II)
• 7) , or , depending on which substitution you used. (You can prove these two are equivalent.) Method: see  PatrickJMT’s first video on Trigonometric integrals.

Answers and hints to Self-Test 2:

• 1) : you must divide first, then integrate
• 2) : integrate by parts twice, then solve for , as in Example 162
• 3) : use substitution
• 4) : integrate by parts
• 5) : use substitution
• 6) : break the integral into two pieces, as in the similar problem on the second quiz. Then use FTC part II with the Chain Rule on each. Here is practice using FTC with the Chain Rule from Khan Academy.
• 7) : use the trigonometric identities to substitute for both and , multiply out and proceed. This is done in the second of PatrickJMT’s videos on Trigonometric integrals  which I have previously recommended to you.