### 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 = y^{2}/2

:.I = (Sin^{2} 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:

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

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

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

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

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

~ Twish ~

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?.

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