# Math172FinalFall19_2 Solutions.pdf - Schumaker Math 172...

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Math 172: Second Semester Calculus Fall Semester, 2019 Final Exam Work must be shown to receive credit. No calculators. sin 2 (࠵?) + cos 2 (࠵?) = 1 tan 2 (࠵?) + 1 = sec 2 (࠵?) sin 2 (࠵?) = (1 − cos(2࠵?))/2 cos 2 (࠵?) = (1 + cos(2࠵?))/2 sin(࠵?/3) = √3 /2 sin(࠵?/4) = √2 /2 sin(࠵?/6) = 1/2 cos(࠵?/3) = 1/2 cos(࠵?/4) = √2 /2 cos(࠵?/6) = √3 /2 If you run out of room working a problem then you can use the blank page on the back. Be sure to leave a note on the original page directing the grader to continue on the back. # 1 2 3 4 5 6 7 8 9 10 11 12 total worth 12 12 12 13 13 12 12 13 13 13 13 12 150 Schumaker Please report any errors
Question 1 (12 points)Find the area bounded by the line ࠵? = ࠵?/3and the graph of ࠵? =࠵?TxtopIntersectionsITXAXpbottomolfXZXX0isonesolution9X9istheDividebytogetGI1otherfoolXYZxzydsolution23312IzX2l83.9312jiz9OIz9212.94213.272Zz . 9
Question 2. (12 points)Find the volume of the solid of revolution generated by rotating the following region about the ࠵?-axis: the region in the first quadrant bounded by the graph of ࠵? = 4 − ࠵?2and the axes. OY Use shells 47 I V So22TXydX y S 2nX 4 xD X I 2 it o4X X3dx 2it 2X 4tx4 o zit 8 tT.l6 0 211 8 4 8