MATH128 Lecture 4: Tutorial-June6
16 Jun 2016
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Problem express the volume of the solid of rotation obtained by rotating the region bounded by about the x-axis as an integral. y = sin x, y = cos x, Solution since our bounding curves are functions of the axis of rotation this is a hint that the method of washers/disks will be most convenient. If we graph the functions we have the following: f (x) = cos(x) g(x) = sin(x) We can see from the gure that cos(x) sin(x) on the interval 0 to . Now in general a volume integral for the disk method has the form. A(x)dx where a(x) describes the disk (washer) area as a function of x. In our case to nd a(x) we need to take the di erence of the area of the disk with radius cos(x) and the area of the disk with radius sin(x). Precisely (recall area of a circle is 2 r2):
