CN202771682U - Exponential function rotating body volume definite integral demonstration instrument - Google Patents
Exponential function rotating body volume definite integral demonstration instrument Download PDFInfo
- Publication number
- CN202771682U CN202771682U CN 201220500792 CN201220500792U CN202771682U CN 202771682 U CN202771682 U CN 202771682U CN 201220500792 CN201220500792 CN 201220500792 CN 201220500792 U CN201220500792 U CN 201220500792U CN 202771682 U CN202771682 U CN 202771682U
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- container
- exponential function
- glass plate
- body volume
- definite integral
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Abstract
The utility model relates to a teaching appliance and discloses an exponential function rotating body volume definite integral demonstration instrument which is mainly formed by a bottom plate, a glass plate, a container and a measuring cup. The bottom plate is vertically connected with the glass plate. The glass plate is provided with a plane rectangular coordinate system. The container is formed by rotating an exponential function y=ex around an x axis of the coordinate system with a half cycle in an interval [0, ln3]. The contained is formed by enclosing a curved surface, a bottom plane and a side plane. The side plane is a part of the glass plate. The container is provided with a water inlet and a water outlet. The water inlet is positioned at a top end of the container, and the water outlet is positioned at a bottom end of the container. The measuring cup is provided with a scale line which indicates a volume of 4pi cubic units. The exponential function rotating body volume definite integral demonstration instrument has the advantages of simple structure and low cost, students can visually and quantitatively understand a geometric meaning of a rotating body volume formed by rotating the exponential function around the x axis in a given interval or the definite integral.
Description
Technical field
The utility model relates to the education and instruction apparatus, a kind of exponential function rotary body volume definite integral demonstration instrument particularly, can make the student very intuitively quantize geographical separate exponential function between the given area in around the rotary body volume of x axle rotation formation or the geometric meaning of definite integral.
Background technology
The student is learning higher mathematics need to ask function curve around rotary body volume that specified coordinate axle rotation forms the time, if intuitively teaching aid demonstration can be arranged, have good effect, described exponential function rotary body volume definite integral demonstration instrument can solve understands rotary body volume that exponential function forms around x axle rotation between the given area or the problem of definite integral geometric meaning quantitatively.
The utility model content
In order to enrich the education and instruction apparatus, solve some apparent problem of definite integral in the higher mathematics, the utility model provides a kind of exponential function rotary body volume definite integral demonstration instrument, can make the student very intuitively quantize geographical separate exponential function between the given area in around the rotary body volume of x axle rotation formation or the geometric meaning of definite integral.
The scheme that the utility model adopts is:
Exponential function rotary body volume definite integral demonstration instrument mainly is made of base plate, glass plate, container, measuring cup, and described base plate is connected with described glass plate is vertical, has plane right-angle coordinate on the described glass plate, and described container is index function y=e
xForm around the x of described coordinate system axle rotation half cycle in interval [0,1n3], its volume is index function y=e
xIn described interval around rotate a circle half of the rotary body volume that forms of the x of described coordinate system axle, described container is surrounded by curved surface and baseplane and side plane, described side plane is the part of described glass plate, described container has water inlet and water delivering orifice, described water inlet is positioned at the top of described container, described water delivering orifice is positioned at the bottom of described container, and described measuring cup has the scale mark that volume is 4 a π cubic units.We know, when the definite integral that learns higher mathematics, for exponential function y=e
xIn described interval [0,1n3] around the x axle rotary body volume that forms that rotates a circle be
Individual cubic units, and the volume of filling the water of described container is 2 a π cubic units, the volume of two described containers just in time is index function y=e
xThe rotary body volume that in described interval [0,1n3], rotates a circle and form around the x axle.
The beneficial effects of the utility model are:
Exponential function rotary body volume definite integral demonstration instrument simple structure cost is low, can make the student very intuitively quantize geographical separate exponential function between the given area in around the rotary body volume of x axle rotation formation or the geometric meaning of definite integral.
Description of drawings
Further specify below in conjunction with figure of the present utility model:
Fig. 1 is described exponential function rotary body volume definite integral demonstration instrument schematic diagram;
Fig. 2 is described measuring cup schematic diagram.
Among the figure, 1. base plate, 2. glass plate, 3. baseplane, 4. side plane, 5. curved surface, 6. water inlet, 7. water delivering orifice, 8. scale mark.
Embodiment
Exponential function rotary body volume definite integral demonstration instrument schematic diagram as described in such as Fig. 1 being, mainly consisted of by base plate, glass plate, container, measuring cup, described base plate (1) and vertical connection of described glass plate (2), have plane right-angle coordinate on the described glass plate, described container is index function y=e
xForm around the x of described coordinate system axle rotation half cycle in interval [0, ln3], its volume is index function y=e
xIn described interval around rotate a circle half of the rotary body volume that forms of the x of described coordinate system axle, described container is surrounded by curved surface (5) and baseplane (3) and side plane (4), described side plane (4) is the part of described glass plate (2), described container has water inlet and water delivering orifice, described water inlet (6) is positioned at the top of described container, and described water delivering orifice (7) is positioned at the bottom of described container.
Measuring cup schematic diagram as described in such as Fig. 2 being, described measuring cup has the scale mark that volume is 4 a π cubic units (8).Water is added from water inlet, and till filling it up with, the water when opening water delivering orifice in the described container is all put into described measuring cup, the volume that at this moment has water in the described measuring cup is 2 a π cubic units; Repeat again above-mentioned add water and discharge water after, can see that the described measuring cup water surface just in time arrives described scale mark (8), has illustrated exponential function y=e
xBetween the given area, be 4 a π cubic units around the x of the described coordinate system axle rotary body volume that forms that rotates a circle in [0, ln3].
Claims (1)
1. exponential function rotary body volume definite integral demonstration instrument, mainly consisted of by base plate, glass plate, container, measuring cup, it is characterized in that: described base plate (1) and vertical connection of described glass plate (2), have plane right-angle coordinate on the described glass plate, described container is index function y=e
xInterval [0, ln3] in form around the x of described coordinate system axle rotation half cycle, described container is surrounded by curved surface (5) and baseplane (3) and side plane (4), described side plane (4) is the part of described glass plate (2), described container has water inlet and water delivering orifice, described water inlet (6) is positioned at the top of described container, described water delivering orifice (7) is positioned at the bottom of described container, and described measuring cup has the scale mark that volume is 4 a π cubic units (8).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 201220500792 CN202771682U (en) | 2012-09-20 | 2012-09-20 | Exponential function rotating body volume definite integral demonstration instrument |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 201220500792 CN202771682U (en) | 2012-09-20 | 2012-09-20 | Exponential function rotating body volume definite integral demonstration instrument |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN202771682U true CN202771682U (en) | 2013-03-06 |
Family
ID=47778241
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN 201220500792 Expired - Fee Related CN202771682U (en) | 2012-09-20 | 2012-09-20 | Exponential function rotating body volume definite integral demonstration instrument |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN202771682U (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105059021A (en) * | 2015-09-01 | 2015-11-18 | 南京工业职业技术学院 | Composite function demonstration and image rendering device |
| CN112233507A (en) * | 2020-09-03 | 2021-01-15 | 常州工学院 | Teaching aid for calculating volume by using infinitesimal method |
-
2012
- 2012-09-20 CN CN 201220500792 patent/CN202771682U/en not_active Expired - Fee Related
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105059021A (en) * | 2015-09-01 | 2015-11-18 | 南京工业职业技术学院 | Composite function demonstration and image rendering device |
| CN105059021B (en) * | 2015-09-01 | 2016-11-30 | 南京工业职业技术学院 | Compound function demonstration and image plotting device |
| CN112233507A (en) * | 2020-09-03 | 2021-01-15 | 常州工学院 | Teaching aid for calculating volume by using infinitesimal method |
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| C17 | Cessation of patent right | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20130306 Termination date: 20130920 |