How do you find the area bounded by the x-axis?

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How do you find the area bounded by the x-axis?

To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. Areas under the x-axis will come out negative and areas above the x-axis will be positive. This means that you have to be careful when finding an area which is partly above and partly below the x-axis.

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 do you find the volume of a solid rotation around 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.

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What is the area bounded by the curve?

We conclude that the area under the curve y = f(x) from a to b is given by the definite integral of f(x) from a to b. f(x)dx. f(x)dx when the curve lies entirely above the x-axis between a and b. Calculate the area bounded y = x−1 and the x-axis, between x = 1 and x = 4.

How do you find the area bounded by two lines?

Answer: The area under a curve that exists between two points can be calculated by conducting a definite integral between the two points. To calculate the area under the curve y = f(x) between x = a & x = b, one must integrate y = f(x) between the limits of a and b.

What is the area bounded by the curve y 2 4x and x2 4y?

The area of the region bounded by the parabolas is 5.33 sq.

How do you find the volume of the solid generated by revolving the region bounded by the graphs?

1 Answer

  1. y=e−x. radius is.
  2. r=e−x. Circular area generated by revolving around x axis is.
  3. A=πr2. volume of the elementary solid of thickness dx is.
  4. dV=Adx. The lower limit is given to be x=0. The upper limit is given to be x=1.
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How do you find the radius of a disk?

The radius is y, which itself is just the function value at x. That is, r = y = f(x). The height of the disk is equal to dx (think of the disk as a cylinder standing on edge).