MT19bMt1_W09.pdf - Math 19B Midterm 1 Version 1 Dr Frank...

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Math 19BMidterm 1Version 11/30/2009 , Dr. Frank B¨auerle, UCSCNote:Show your work. In other words, just writing the answer,even if correct, may not be sufficient for full credit. Scientific calcula-tors are allowed, but no programmable and/or graphing calculators.Your Name:Your TA’s Name:Problem 1:out of 35Problem 2:out of 10Problem 3:out of 5Problem 4:out of 20Problem 5:out of 5Problem 6:out of 10Problem 7:out of 15Total:out of 100Good luck and have a good weekend!1
1. (35 points) Evaluate the following definite and indefinite integrals. If anintegral does not exist, explain why.(a)x2(x+ 5)dx(b)π402e1 +e2dx(c)tsin2(ωt2) cos(ωt2)dtwhereωis a positive real number constant.2
(d)41cos(t)tdt(e)1-21u2du(f)1-1z91 +z20dz(Think!)(g)1arctan(x)·(1 +x2)dx3
2. (10 points) The velocity functionv(t) = 2 sin(πt4) is given for a particlemoving (back and forth) on a straight line. Assumev(t) is measured inmeters per second. Find the following:(a) The displacement of the particle between timet= 1 and timet= 6.(b) The total distance traveled by the particle between time

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