Let R be the region bounded by the following curves. Find the ...

Question

Let R be the region bounded by the following curves. Find the volume of the solid generated when R is revolved about the given line.

x=2−secy,x=2,y=π/3, and y=0; about x=2

Accepted Answer

Let T be the region bounded by X equals 3 minus C Y, X equals 3, Y equals 0, and Y equals pi divided by 6. Find the volume of the solid generated when T is evolved about the line X equals 3. We're also given a graph with all of our bounding lights. Now, to solve this, we're going to make use of the disc method for volume. In this case, you will have our volume. Equals the integral from A to B. Of pi multiplied. By radius square. DY No. We need to find what radius is. Radius is given by the distance from X equals 3 to X equals 3 minus sequent of Y. We can write this then as 3 minus 3 minus the sequent of Y. We can simplify this. And we end up getting 3 minus 3 plus sequent Y or just sequent Y by itself. Meaning Our integral turns into pi multiplied by sequent Y squared. Do what? And this is just pi multiplied by sequence squared Y. Now, we also need the balance. It tells us Y goes from 0 to pi divided by 6, so we replace our bounds with those values. Now we can solve. We know the integral of sequin squared is actually a known equation, which is tangent. So, we will say this turns into pi, multiplied. By a tangent way From 0 to pi divided by 6, meaning we get pi multiplied. By the tangent of pi divided by 6 minus the tangent of 0. We cannot simplify. We know the tangent of pi divided by 6 gives us 1 divided by the square root of 3. tension of 0 gives us 0. Meaning our final answer. Ends up being pie. Divided by the squared of 3, or pi multiplied. By the square root of 3 divided by 3. Because this is volume, our answer is in cubic units. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

Let R be the region bounded by the following curves. Find the volume of the solid generated when R is revolved about the given line.x=2−secy,x=2,y=π/3, and y=0; about x=2

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Let R be the region bounded by the following curves. Find the volume of the solid generated when R is revolved about the given line.

x=2−secy,x=2,y=π/3, and y=0; about x=2