Integration can be used to calculate the area under a curve and the volume of solids of revolution.
It could be a Gaussian curve (Normal distribution) rotated through a right angle.It could be a Gaussian curve (Normal distribution) rotated through a right angle.It could be a Gaussian curve (Normal distribution) rotated through a right angle.It could be a Gaussian curve (Normal distribution) rotated through a right angle.
Geometrically the definite integral from a to b is the area under the curve and the double integral is the volume under the surface. So just taking the integral of a function does not yield the volume of the solid made by rotating it around an axis. An integral is only a solid of revolution if you take an infinite sum of infinitesimally small cylinders that is the disk method or you do the same with shells.
geometically , the definite integral gives the area under the curve of the integrad .
The Cartesian plane allows geometric information to be converted to a coordinate system which can then be analysed using algebraic techniques. Conversely algebraic information can be converted (by plotting) to a geometric form. Theorems that have been proved in one of these two disciplines can be used to solve problems in the other. Thus finding the volume when a curve is rotated becomes a simple matter of integration. Solving simultaneous equations is reduced to finding the point of intersection (if any) of the corresponding graphs.
Integration can be used to calculate the area under a curve and the volume of solids of revolution.
It could be a Gaussian curve (Normal distribution) rotated through a right angle.It could be a Gaussian curve (Normal distribution) rotated through a right angle.It could be a Gaussian curve (Normal distribution) rotated through a right angle.It could be a Gaussian curve (Normal distribution) rotated through a right angle.
Geometrically the definite integral from a to b is the area under the curve and the double integral is the volume under the surface. So just taking the integral of a function does not yield the volume of the solid made by rotating it around an axis. An integral is only a solid of revolution if you take an infinite sum of infinitesimally small cylinders that is the disk method or you do the same with shells.
If this is on mymaths.co.uk then the answer to this question is: Integration. That is how to find the area under the curve.
By integration. Divide the curve into small pieces, then add up the length of all the pieces.
geometically , the definite integral gives the area under the curve of the integrad .
"integration"
Integration.
Around 4°C, the curve of volume vs. temperature is horizontal, meaning that for small changes in temperature, the volume will NOT change.
The Cartesian plane allows geometric information to be converted to a coordinate system which can then be analysed using algebraic techniques. Conversely algebraic information can be converted (by plotting) to a geometric form. Theorems that have been proved in one of these two disciplines can be used to solve problems in the other. Thus finding the volume when a curve is rotated becomes a simple matter of integration. Solving simultaneous equations is reduced to finding the point of intersection (if any) of the corresponding graphs.
if its the mymaths one type integration into the box!
What about the ringer volume? when the phone rings it's too low how do I increase it