Math 1B Section 112 Quiz #5Thursday, 27 September 2007Theo [email protected]:1. (3 pts) Find the length of the curve y = ln(cos x) as x ranges between 0 and π/4.length of curve =Rπ/40p1 + (y0)2dx .5 pt=Rπ/40p1 + (−sin x/ cos x)2dx .5 pt=Rπ/40sec x dx 1 pt= ln(sec x + tan x)|π/40.5 pt= ln(2/√2 + 1) − ln(1) .5 pt= ln(1 +√2)2. (3 pts) Find the area of the surface of revolution generated by rotating the curvey = x3, as x ranges between 1 and 3, around the x-axis.area of surface = 2πR31yp1 + (y0)2dx .5 pt= 2πR3x=1x3√1 + 9x4dx .5 pt= 2πR1+9·34u=10√udu361 pt=π1823u3/2270101 pt=π27(7303/2− 103/2)13. (4 pts) Find the area of the surface of revolution generated by rotating the curvey =ex+ e−x2= cosh x, as x ranges between 0 and 2, around the y-axis.area of surface = 2πR20xp1 + (y0)2dx .5 pt= 2πR20xr1 +ex−e−x22dx .5 pt= 2πR20xq2+e2x−1+e−2x4dx= 2πR20xex+e−x2dx 1 pt= πR20xexdx + πR20xe−xdx= π [xex− ex]20+ π [−xe−x− e−x]201.5 pt= πe2+ 1 − 3e−2+ 1= 2π + πe2− 3π/e2.5
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