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Monday, May 29, 2006

INdefinite INtegral is INexplicable

To integrate:
Sin x .Cos x dx

Let I=integral of sinx.cosx dx

(1) Let Sin x = y

Differentiating both sides:

Cos x dx = dy

:. I=integral of y dy

:. I = y2/2

:.I = (Sin2 x)/ 2

(2) Sin x .Cos x = (Sin2x)/2

:. I = integral of (1/2)*(Sin2x) dx

=integral of (¼)*(Sin2x) d(2x)

I = - (1/4)*(Cos 2x)

HOW DO WE GET DIFFERENT RESULTS FROM TO DIFFERENT METHODS?

6 comments:

saurya_time_travel said...

dear pravar,
i am not good at maths but see this
If u analyse both the answers, u get these two things
1/4 - cos2x/4 and - cos2x/4

it is the integration constant which is different in both cases that is making the answers different. If u do the definite integration u will find both answers same ...

time

bravura said...

hey mate,
i hav very little knowledge of calculus but i would still try to explain this.
Through my little knowledge of calculus i know that when you do indefinite integral you have to introduce a constant. I think the results are different because u haven't introduced the constants. I think if u do that the results will be the same.
Swetabh

saurya_time_travel said...

right bravura,
when integrating over a given range, the constsnt term will take care of the answer. it will be the same in both cases.

time

Gr81 said...

Thats solves the problem... Thnx to TIME!!
We are getting a gr8 response from u guys - Keep Posting and commenting!!
SwItCh On YoUr FuSeD BuLbS!!!
;)
--
Rash The Gr81

TwIsTeR said...

I agree with you guys... just to make the scenario crystal clear, I've added a post on this thing! C it guyz ....

~ Twish ~

Antiderivative of cosx said...

I think maths introduce more than one procedure to solve problems,your try is very impressive,but it is a common technique.Could you mention more example for this procedure?.