Sketch the region bounded by the graph of the equations and determine the area of the region

Y = sinx y = cosx π/4≤ x ≤ 5π/4

Find the area of the region bounded by the following:

Y =x² - 4x + 3 y = x³ x = 0

The table show s the annual service revenue R1 in billions of dollars for the cellular telephone industry for the years 1995 through 2001.

a) Use the regression capabilities to find an exponential model for the data. Let t represent the year, with t=5 corresponding to 1995

b) A financial consultant believes that a model for service revenue for the years 2005 through 2010 is

R2 = 5 + 6.83e.2t

What is the difference in total service revenue between the two models for the years 2005 through 2010.

Year 1995 1996 1997 1998 1999 2000 2001

R1 19.1 23.6 27.5 33.1 40.0 52.5 65.0

Find the volume of the solid generated by revolving the plane region bounded by the equations and indicated lines:

Y = 1 y = 0 x = 2 x = 6 (1 + √x-2 )

Find the volume of the solid of y = x√x+1 and y = 0 generated by revolving the region about:

a) x-axisb) Y-axis

A gasoline tank is an oblate spheroid generated by revolving the region bounded by the graph of x²/16 + y²/9 = 1 about the y-axis, where x and y are measured in feet. Find the depth of the gasoline in the tank when it is filled to one fourth its capacity. (note volume is 64π)

Find the arc length of the graph of the function over the given interval:

F(x) = 4/5 x5/4 [0,4]

The region bounded by the graph of y = 2√x y = 0 x = 3 is revolved around the x-axis. Find the surface are of the solid generated.