Common questions

How do you find the volume of a curve rotated around an axis?

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How do you find the volume of a curve rotated around an axis?

Answer: The volume of a solid rotated about the y-axis can be calculated by V = π∫dc[f(y)]2dy. Let us go through the explanation to understand better. The disk method is predominantly used when we rotate any particular curve around the x or y-axis.

What does rotated about the X axis mean?

Rotation About the x-axis Integration can be used to find the area of a region bounded by a curve whose equation you know. If we want to find the area under the curve y = x2 between x = 0 and x = 5, for example, we simply integrate x2 with limits 0 and 5.

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What is the volume of an infinitesimal disk obtained by rotating y x2 about the X − axis?

Disc method around x-axis (video) | Khan Academy.

How do you do the washer method?

How to Find the Volume of a Shape Using the Washer Method

  1. Determine where the two curves intersect.
  2. Figure the area of a cross-sectional washer.
  3. Multiply this area by the thickness, dx, to get the volume of a representative washer.
  4. Add up the volumes of the washers from 0 to 1 by integrating.

How do you find the axis of a rotation matrix?

For non-symmetric matrices, the axis of rotation can be obtained from the skew-symmetric part of the rotation matrix, S=. 5(R−RT); Then if S=(aij), the rotation axis with magnitude sinθ is (a21,a02,a10).

What is the axis of rotation for x = 2?

The axis of rotation, x = 2, is a line parallel

How do you find the volume of a solid?

Example 2 Determine the volume of the solid obtained by rotating the portion of the region bounded by y = 3√x y = x 3 and y = x 4 y = x 4 that lies in the first quadrant about the y-axis. First, let’s get a graph of the bounding region and a graph of the object.

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What is the difference between the axis of rotation and inner radius?

So, we know that the distance from the axis of rotation to the x x -axis is 4 and the distance from the x x -axis to the inner ring is x x. The inner radius must then be the difference between these two.

Is area a function of x x or Y Y?

Also, in both cases, whether the area is a function of x x or a function of y y will depend upon the axis of rotation as we will see. This method is often called the method of disks or the method of rings. Let’s do an example.