Let S be the solid with ?at base, whose base is the region in the xy plane de?ne

Question

Let S be the solid with ?at base, whose base is the region in the xy plane de?ned by the curves y=ex, y=?2, x=1 and x=2, and whose cross-sections perpendicular to the x axis are semi-circles with diameters that sit in the xy plane.

b) Find the volume of S with ±0.01 precision.

Let S be the solid with flat base, whose base is the region in the y plane defined by the curves ye perpendicular to the x axis are semi-circles with diameters that sit in the c y plane a) Find the area A(x) of the cross-section of S given by the semi-circle that stands perpendicular to the z y plane, at coordinate , y =-2, x = 1 and z 2. and whose cross-sections A(x) (Exact formula) (We must write e Az for ex , en(2 * z-1) for e2z-1,etc) b) Find the volume of S with +0.01 precision. Answer Number

Explanation / Answer

solution:

i)length of base = diameter of semicircle=2r =e^x +2

A(x) = pi(r^2)/2 =pi* [((e^x +2)/2)^2]/2

A(x) =(pi/8)(e^x +2)^2

ii) volume s = [0 to 2] integral (pi/8)(e^x +2)^2 dx

=[0 to 2](p/8) integral e^2x +4e^x +4 dx

=[0 to 2](p/8) [ (e^2x)/2 +4e^x +4x +c]

=(pi/8) *([(e^4)/2 +4e^2 +8 ] -[ 1/2 +4 +0 ])

=23.70

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