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mercedesamatap21hx0
26.07.2019 •
Mathematics
Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(6x), y = 4, y = 6, x = 0; about the y-axis step 1 we will use horizontal strips. such a strip has a vertical span of δy. sketch the region.
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Ответ:
V = 2219.08π
Step-by-step explanation:
If you use the washer/disk method as you indicated you were going to in the statement "we will us horizontal strips", you have to solve that equation for x. The equation solved for x is
The bounds are y-intervals from 4 to 6, and we are rotating about the y-axis. I cannot sketch the graph for you here, but if you need it, graph y = ln(6x) and you'll see what it looks like. I can only help you with the calculus of it, not the drawing of it.
The volume formula then for this is
Squaring what's inside the parenthesis gives you:
To make this a tiny bit simpler we can pull out the fraction:
The antiderivative of e to the 2y power is found:
We can then pull out the 1/2:
Evaluating that antiderivative using the First Fundamental Theorem of calculus gives you:
If you leave your answer in terms of pi it is:
2219.08π or if you multiply pi in it is:
6971.44863
Ответ:
2y = 80 degrees
y = 40 degrees