Calculus II                                                    Quiz #3                            March 11, 2005

Name____________________              R.  Hammack                               Score ______

(1)     Consider the illustrated region which lies between the graphs of y = sin(x) and y = cos(x).  Find the area of this region.


∫_ (-3π/4)^(π/4)(cos(x)-sin(x)) dx=[sin (x) + cos (x)] _ (-3π/4)^(π/4)=sin(π/4)+cos(π/4)-sin(π/4)-cos(π/4)=1/2^(1/2)+1/2^(1/2)+1/2^(1/2)+1/2^(1/2)=4/2^(1/2)=22^(1/2)square units

(2)    Consider the region contained between y=x^2,  x=0, x=2, y=0. Find the volume of the solid obtained when this region is rotated around the x-axis.

∫_0^2π(x^2)^2dx=∫_0^2π x^4dx=[π x^5/5] _0^2=π 2^5/5=32/5π cubic units