Rob Bayer Math 1B PDP Worksheet January 27, 2009
Instructions
1. Introduce yourselves!
2. Find some blackboard space, a piece of chalk, and decide who will be your first scribe.
3. Do the problems below, having a different person be the scribe for each one.
Trig Integrals I
1. Find Zsin xcos xdx
(a) By making a u-substitution
(b) By integrating by parts
(c) By using an identity
(d) Are your answers the same?
2. Zsin3xcosπxdx
3. Zπ/4
−π/4
tan5(x) sec3(x)dx
4. Z1−tan2(x)
sec2(x)dx
5. (a) Find the average value of sin2xbetween 0 and 2π.
(b) Now sketch a graph of sin2x. Does your answer seem reasonable?
6. For this problem, m,nare non-negative integers
(a) Determine whether each of the following are even or odd: 2m+ 1,4n−3,6m, 2n2+ 1
(b) Find a general formula for Rsin2n+1 xcosmxdx
(c) Find a general formula for Rsec2nxtanmxdx
Trig Integrals II
1. Zsin(4x) sin(3x)dx
2. Zcos(4x) sin2(3x)dx
3. Zxcos(2x2+ 3) sin(3x2
−1)dx
Extra Problems If you finish early, take a stab at these.
1. Zcos x−1
cos x+ 1dx
2. Find the volume of the solid obtained by rotating y= sin xbetween x= 0 and x=π
(a) about the y-axis
(b) about the x-axis
3. Find Zsin x+ cos x
sin 2xdx
4. Find the average value of sin2xcos2xover one period. Now do the same for sin4x