Calculus II
Quiz #6
March 22, 2002
Name:____________________
R. Hammack
Score: _____


(1) Evaluate the following integrals.
(a) [Graphics:Images/quiz6sol_gr_1.gif][Graphics:Images/quiz6sol_gr_2.gif][Graphics:Images/quiz6sol_gr_3.gif][Graphics:Images/quiz6sol_gr_4.gif][Graphics:Images/quiz6sol_gr_5.gif][Graphics:Images/quiz6sol_gr_6.gif]

u = 5x
du = 5 dx

(b) [Graphics:Images/quiz6sol_gr_7.gif][Graphics:Images/quiz6sol_gr_8.gif]= [Graphics:Images/quiz6sol_gr_9.gif][Graphics:Images/quiz6sol_gr_10.gif]

  u =   x      dv = cos(3x)dx
du = dx        v = [Graphics:Images/quiz6sol_gr_11.gif]



(c) [Graphics:Images/quiz6sol_gr_12.gif][Graphics:Images/quiz6sol_gr_13.gif][Graphics:Images/quiz6sol_gr_14.gif]=[Graphics:Images/quiz6sol_gr_15.gif]

u =   [Graphics:Images/quiz6sol_gr_16.gif]          dv = [Graphics:Images/quiz6sol_gr_17.gif]dx
du = 2x dx        v = [Graphics:Images/quiz6sol_gr_18.gif]


(d) [Graphics:Images/quiz6sol_gr_19.gif][Graphics:Images/quiz6sol_gr_20.gif][Graphics:Images/quiz6sol_gr_21.gif]
[Graphics:Images/quiz6sol_gr_22.gif][Graphics:Images/quiz6sol_gr_23.gif][Graphics:Images/quiz6sol_gr_24.gif]
[Graphics:Images/quiz6sol_gr_25.gif][Graphics:Images/quiz6sol_gr_26.gif]=[Graphics:Images/quiz6sol_gr_27.gif]

u = sin x
du =
cos x dx


(2)
Find the area under the graph of [Graphics:Images/quiz6sol_gr_28.gif], and between x = 1 and x = 2.

[Graphics:Images/quiz6sol_gr_29.gif][Graphics:Images/quiz6sol_gr_30.gif][Graphics:Images/quiz6sol_gr_31.gif][Graphics:Images/quiz6sol_gr_32.gif][Graphics:Images/quiz6sol_gr_33.gif]
[Graphics:Images/quiz6sol_gr_34.gif]
[Graphics:Images/quiz6sol_gr_35.gif]1/2 square unit