Setting up an integral of rotation is used as a method of of calculating the volume of a 3D object formed by a rotated area of a 2D space. Finding the volume is similar to finding the area, but there is one additional component of rotating the area around a line of symmetry.

<span>First the solid of revolution should be defined. The general function is y=f(x), on an interval [a,b].</span>

Then the curve is rotated about a given axis to get the surface of the solid of revolution. That is the integral of the function.

<span>It all depends of the function f(x), which must be known in order to calculate the integral.</span>

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2 years ago

Crystals are made using supersaturated solutions of solids in water.

labwork [276]

The way these supersaturated solutions are made is: A. The water would need to be heated to a higher temperature, which would give molecules and ions more kinetic energy, increasing solubility.

Solubility is simply a measure of how readily a substance is able to dissolve in a solvent to form a solution. Thus, a substance is soluble when it dissolves completely in a solvent and it is considered to be insoluble when it does not dissolve in a solvent or if it only dissolves partially.

A supersaturated solution can be defined as a solution that contains more solute than the equilibrium amount.

Generally, supersaturated solutions of solids in water are typically used for the creation of crystals because they are able to hold more of the solute than they would at room temperature.

In order to create these supersaturated solutions, the water should be heated to a higher temperature, so that the water molecules and ions can gain more kinetic energy and thereby increasing solubility.

In conclusion, heating the water to a higher temperature causes the water molecules and ions to gain more kinetic energy and thereby increasing solubility..