Multiple integrals and its significance

Triple integral is used to find the volume of solids.

similarly double integral is for finding areas enclosed between irregular curves.

but the requirement is that the integration should take place within specified limits.

But single integrel reptesents area enclosed.between two graphs. And.double.intg denotes volume covered by a surface?

VISHNUGOPANBut single integrel reptesents area enclosed.between two graphs. And.double.intg denotes volume covered by a surface?

no single integral only represents the length of a line and not area.

as long as the integration is within limits.

Thread moved to mathematics section.

zaverino single integral only represents the length of a line and not area.

as long as the integration is within limits.

consider the function y=3. integrating this from 2 to 5 gives result 9 which is the area under the graph. not the length of the line.

VISHNUGOPANconsider the function y=3. integrating this from 2 to 5 gives result 9 which is the area under the graph. not the length of the line.

In this case the area is found between the four straight lines , y=3, x=2, x=5 and the x-axis (y=0).

all four of these are straight lines and the area is determined easily.

But if an area is enclosed by more than two complicated curves , lets say y=x^3 and y=x^2 , then single integration becomes complex, and thus the double integration method is sought for making the procedure simple.

Just to add in more to zaveri's content, You can derive all the formulas used to compute volume and area using Integration. Give it a try, then you would come to know how they are derived.

zaveriIn this case the area is found between the four straight lines , y=3, x=2, x=5 and the x-axis (y=0).

all four of these are straight lines and the area is determined easily.

But if an area is enclosed by more than two complicated curves , lets say y=x^3 and y=x^2 , then single integration becomes complex, and thus the double integration method is sought for making the procedure simple.

thank you sir

the main purpose of integration is

single = length of a curve ( in radius of curvature calculations)

double = area enclosed by two curves

triple = volume of solid bounded by curves

VISHNUGOPANconsider the function y=3. integrating this from 2 to 5 gives result 9 which is the area under the graph. not the length of the line.

What do you mean by area under the graph? Graph consists many grids right? So it is a two dimensional region. what you say is a misnomer I suppose.You have to visualise multiple integrals. As variables increase, obviously its representation or dimensions also increase. So, the multiple integral shows its head.! Significance? It has infinite applications in science, engineering and Economics.! 😀