Geometrical interpretation indefinite integrals (Part - 4) - Integrals, Maths, Class 12 Video Lecture

hello friends this video on integrals
part 4 is brought you by exam clear calm
no more fear from exam before watching
this video please make sure that you
have watched part 1 2 part 3 now let's
understand the geometrical
interpretation of indefinite integral so
let's suppose I have my function FX is
you can do 2x if I want to find
integration of this that is nothing but
FX dot DX and there is nothing but 2 X
dot DX correct and the rhythm ought to
be X becomes X square by 2 plus C so
this is nothing but Y is X square plus
some constant K so this is the
integration of FX is going to do X I can
take any value of K if I take K is equal
to 0 my equation becomes y is equal to X
square if I take K is equal to 1 my
equation becomes Y is going to XK plus 1
if I take K is equal to 2 this becomes X
square plus 3 so I take Y is equal to
minus 1 this becomes Y as Delta X square
minus 1 so there's so many equations
which you can form from integration of
this equation so let's plot all these
graphs so Y is going to expel with
something like this something like this
correct y is equal to X square plus 1 do
something like this draw it do something
like this really my is going to expect
less room like this y is going to
exclaim and something like this right so
many graphs you get so many grass and is
all integration of y is equal to FX and
this is one thing common that is you
take any point here let's suppose X is
going to 1 you draw a line from this X
go to one pile and YX is and you take
any points in this
the slope at all these points will be
slave there is all this line l1 l2 l3 l4
l5 they'd all be paddle okay and that is
how we represent this graph geometrical
this integration geometrically so if I
have my function FX / 2x my
intentionally what X square plus K I can
take any value of K so you get so many
grass but there is one common thing that
is all these graphs are identical they
are just nothing but you move this draft
up and down in this y-axis that's all
and if you take any point and you take a
draw horizontal line you find the slope
you'll see that the slopes are all same
that is all these graphs you get is
identically collapsed and reverse way
also true if you do any of these graphs
you find the D by D and the
differentiation of this you get the same
value that is you take definition of any
of these you get you find f of any of
this you get to see a motherless 2x that
is nothing but slow Q X constant
anything correct that is how genetically
you represent these are the graphs so
many graphs we have you can see these
are the graphs we have and the slope is
2x there is differentiation of this and
if you see but all these is grab the
slope is constant at any point thank you
visit exam viacom to watch free
educational videos try free online tests
get the best quality study materials
study from the best tutors and mentors
and much more
thanks on screen