Question

What is the definite integral ? Can someone help me learn about it ?

Answer 1

Yeah, it's basically an infinite sum of infinitely small things. This seems kinda silly, but you are probably familiar with the concept that a line has no width. Well really it's like an infinitely small width so if you are to like look at a bunch of circles inside each other (pretend this looks pretty) and if you eventually imagine an infinite number of of these circles inside there you'd eventually fill up the area of a circle.

What I'm saying is through a definite integral you can derive the area of a circle\[\Large A= \pi r^2\] from the circumference of it \[\Large C=2 \pi r\] Since you are probably familiar with the idea that an integral is an "anti derivative" that means it goes the other way around, so there's one concrete example as proof that it really is the "anti derivative" by undoing the integral with a derivative: \[\Large \frac{d}{dr}(\pi r^2) = 2 \pi r\]

Answer 2

Sir, can I draw a tangent like we do in ordinary methods ?

Answer 3

Oh, what do you mean? Whereas a derivative can be interpreted as the slope of the tangent line at every place on a function, the definite integral can be interpreted as the area beneath a function over an interval.

Answer 4

Sir..I didn't get it...how?

Answer 5

an integral is a summing of small areas
a definite integral is one which has an answer so you give it a range from say 1 to 5