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It helps to understand the integral - more specifically, the definite integral - as "adding together many pieces". If you cut up a volume into thin slices... Well, you can cut it up in many different ways, but one way this is commonly done is using parallel slices. In this case, for each of the parallel slices you basically need to figure out its area (times the thickness, expressed by "dx" or some other variable with a "d" in front) - and then you need to add all the slices up, i.e., integrate.
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How do you calculate the surface area or volume of each shape?
we can use integration.- multiple integration.
Applications of integral calculus?
Integration can be used to calculate the area under a curve and the volume of solids of revolution.
How do you find volume of an irregular solid figure?
By integration - you divide the figure into many thin slices, and calculate the volume of each slice individually. The volume of each slice, again, can be calculated by integration: divide it into thin rectangles, and calculate the area of each rectangle. If you have a irregular solid figure just immerse it in water and measure the displacement. a la Archimedes
What method find regular solid volume?
Geometry, or algebra (integration).
How could you work out the volume of an irregular shaped object?
One method is to use the water displacement technique. Submerge the object in a graduated cylinder or container partially filled with water, then measure the increase in water volume. This increase in volume equals the volume of the irregular object.
Show by integration the formula of volume of a sphere?
Volume of a sphere in cubic units = 4/3*pi*radius3
What is the use of integration in your practical life?
Google " volume of revolution " problems and see how integration makes these problems that would not be easily solved by other methods easier.
Are summation and integration are same?
Integration uses a summation in the definition of the definite integral, so they are not the same, but they are related. They both yield a type of sum, or area (in the case of integration).
What is the formula to calculate volume of an irregular shape?
By integration, which basically means dividing the object into small slices and calculating the area of each slice. If the (basically 2-dimensional) slice is itself irregular, you need to apply integration once more on each slice. This topic is explored in detail in calculus courses.
How can you obtain a cell's ratio of surface area to volume?
To obtain the ratio of surface area to volume, divide the surface area by the volume.
Who discovered the volume of cylinder?
Archimedes. Archimedes published a work named "On the Sphere and Cylinder", where he proved the formulas for the surface area and volume of both spheres and cylinders. This is actually quite impressive, considering that he lacked the concept of calculus or limits to aid him. In calculus, the proof for the volume of a cylinder because trivial through integration by slicing.
Why is the volume of pyramid is only one third of the volume of the prism?
This is easiest shown through integration. If you don't know how to do integration, divide the pyramid into many thin layers, and assume that each is a rectangular block. Try to do this experiment with the help of a spreadsheet like Excel.
