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While I searching for the answer to this question, I totally confused. Atlast I reach in one thing that we may compute some volume integrals by using double integral but to evaluate a triple integral we should go through all the three integrals.
For example, by calculating the surface of a circle, using an integral.
First we have to evaluate the inner integral using ILATE method and then evaluate the outer integral
mass (on a triple-beam balance) volume (water displacement, calculate it with a ruler) density (mass/volume) color transparency state of matter
To find its volume you can find its mass using a triple beam balance and it's density with a graduated cylinder and use the formula v=m/d
Finding the volume of many odd shapes is only possible with integral calculus. Google " volume of revolution. "
Using every-day definitions, it has one face and no edges. However, the answer will be different using topological definitions used for the Euler characteristic.
Do a line integral.
For mass, you would use a triple-beam balance. For volume, you would either use a graduated cylinder (for liquids), calculate the displacement with a graduated cylinder (for an odd-shaped solid), or calculate it using the equation for volume (for a regularly-shaped solid).
The integral of ln(x2) is 2x[ln(x) - 1] + C Do this using the method of integration by parts.
IF you knew the volume of the block and the density of the material it was made of you could calculate it mass (mass = density * volume) but it is normal to measure the mass of something using a mass balance.
It is a way to approximate a definite integral using trapezoids.