How do you find the volume of a function that rotates about the y 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.
How do you rotate the y axis?
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite. When working with the graph of y = f (x), replace x with -x. Reflection in y = x: When you reflect a point across the line y = x, the x-coordinate and the y-coordinate change places.
How do you find the area between two curves on a calculator?
How to Use the Area Between Two Curves Calculator?
- Step 1: Enter the smaller function, larger function and the limit values in the given input fields.
- Step 2: Now click the button “Calculate Area” to get the output.
- Step 3: Finally, the area between the two curves will be displayed in the new window.
What is the volume of the solid generated when the region bounded by the graph of y 2x?
64π15
The volume of the solid generated by y=2x , y=x2 revolved about the x-axis is 64π15 .
How to find the volume of the area between two curves?
Let A 1 be the area between the y -axis and y = x 3, and let A 2 be the area between the y -axis and y = 3 x + 2. The total volume, V T, will be found by V 1 − V 2; where V 1 is the volumes found by revolving A 1, and V 2 is the volume found by revolving A 2. But the expected answer is 56 5 π.
How to calculate the volume of a solid?
For each of the following problems use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by the given curves about the given axis. Rotate the region bounded by y = √x y = x , y = 3 y = 3 and the y y -axis about the y y -axis.
Is the 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.
Which is the distance from the axis of rotation to the inner ring?
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. Or, The outer radius works the same way. The outer radius is,