Test 1D NC Solutions - Test 1D MAT 272 FA15 Name Non-Calculator Portion(50 points There are 100 minutes for the entire test 1 Evaluate the following

Test 1D NC Solutions - Test 1D MAT 272 FA15 Name...

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Test 1D MAT 272 FA15 Name: __________________________________________________ Non-Calculator Portion (50 points). There are 100 minutes for the entire test. 1.Evaluate the following integral. (10 points) . 2.Evaluate the following integral. (10 points) 5 5 5
3.Evaluate the following integral. (10 points) 3࠵?√16−࠵?2࠵?࠵? =34∫ csc(࠵?) ࠵?࠵? = −34ln|csc(࠵?) + cot(࠵?)| + ࠵? = − 34ln |4+√16−࠵?2࠵?| + ࠵? . 3 3 3 4.Evaluate the following integral. (10 points) ∫ tan(6࠵?) sec4(6࠵?) ࠵?࠵?Using the strategy for even powers of secant we get: ∫ tan(6࠵?) sec4(6࠵?) ࠵?࠵? = 12tan2(6࠵?) +124tan4(6࠵?) + ࠵?Using the strategy for odd powers of tangent we get: ∫ tan(6࠵?) sec4(6࠵?) ࠵?࠵? = 24sec4(6࠵?) + ࠵?Both answers are equivalent. 1 1
5.Evaluate the following integral. Leave your answer in exact form. (10 points) ࠵?2࠵?3+ 16࠵?࠵?21This is a basic ࠵?-substitution! Let ࠵? = ࠵?3+ 16࠵?2࠵?3+ 16࠵?࠵?21= 3࠵?࠵?࠵?2417=13[ln|࠵?|]1724=13[ln(24) − ln(17)]=13ln (2417) . 1

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