Unformatted text preview: MAT 2020 Term 11, 10-11 LAB 8
(Thurs, Feb 3) PART I. AREAS AND VOLUMES: THINKING X AS A FUNCTION OF Y
INSTEAD OF Y AS A FUNCTION OF X Sometimes for these problems it’s easier to deal with ftmctional boundaries on the left and right
instead of the top and bottom. In this case we have to think of the boundaries in terms of x = ﬂy) and integrate with respect to y. Here’s the stereotypical case. d
The integral for the area would be I ( f ( y) — g(y))ajz . Note that the function on the right of the picture is the “higher” function (the x values are larger.). For instance to ﬁnd the area bounded by the curves x = 2y2 and x = 4 + yz.
[Recall that implicitplot needs to be used when you do not have equations that give y as a function of x. For instance, im lici lot([x = 2*yA2, x = thy/‘2], x = 0 .. 10, = —5 .. 5)].
P tP Y X :gLyL L7 197 2
Then the integral is f (4+ y2)—(2y2)dy. 1
—2 Sometimes areas can be calculated either way. For instance for the area bounded by the curves
y = 2x and y = x2. Ifwe think y as a function ofx, i 7:1Xj ...
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- Fall '10