This Lab is to be worked in the Math Lab when an instructor is present. You may work with your classmates, but be sure to complete your own assignment to turn in. Clearly document your work. Make sure to include your units and include complete sentences where necessary. Please box/highlight your answers. 1) a. Find S sin 0 cos 0 de by substituting u = sin 0. b. Now find S sin 0 cos 0 de by substituting u = cos 0. c. There is another way of finding this integral which involves the trig identity sin(20) = 2 sin 0 cos 0. Now find S sin 0 cos e de by using the trig identity and substituting u = 20. 2) A bacteria population starts with 400 bacteria and grows at a rate of r(t) = (450.268) e1.12567t bacteria per hour. How many bacteria will there be after three hours? Evaluate the indefinite integrals: 3) f xsin(x2) dx 4) fx2ex dx 5) f (x + 1) v2x + x2 dx 6) S (x2 + 1)(x3 + 3x) +dx t = 0 7 0 = - 1 Evaluate the definite integrals: t = 1 7 V = 2 7) So ( 3t - 1) 50 = [ -050 250 150 50 50 8) So (xe -x2) dx 9) So" * sin (4t) at ) cos( u) du = U = 46 du = 4dt du= dt 10) Se dx 4 x In(x)