can you explain about integral?

Answer 1

In calculus, an integral is the area between two curves. (if there's only one curve, the second is taken to be the x-axis usually.)
It is also called an anti-derivative as it is the opposite of derivatives, i.e. a derivative of an integral of a function is the same as the function itself.

for more, go here; http://en.wikipedia.org/wiki/Integral

Answer 2

Integrals and derrivatives are part of calculus and are about motion and volume. Integrals are a way to find 3D volume area of a shape.

Think of it this way. If you have a cardboard cutout of a balloon, you have the 2 dimensions. If you wanted to find the volume area of a full balloon, the way you could do that is to rotate the cardboard balloon cutout really fast and it would have the shape of a full real balloon. An integral assumes you are rotating that the 2d shape function and creates 3d volume function.

The reason you need this is that you only know how to calculate volumes on cubes (L x W x H) and spheres (PI r CUBED). Any other shape, you couldn't figure out the volume without an integral.

Answer 3

The Riemann-Stieltjes integral I assume? There are multiple integrals, that one is the most common. Second most common is the Lebesgue integral, a more analytical tool useful to mathematicians.

The Riemann integral is the limit of the Riemann sums as the number of equally spaced partitions approaches infinity. If you do not know what a Riemann sum is then you were not taught properly. This is highly likely if you're in a "just calculate and don't think" engineering class as opposed to a "you should be able to explain the calculation before doing it" mathematics course.

Answer 4

the integral is a measure of a set.

Answer 5

integration is the inverse process of differentiation
integration is nothing but summation
while differential calculus helps you find instantaneous values from an overall picture integral calculus helps you to get the macroscopic picture from the microscopic one