Diyadiya
  • Diyadiya
Evaluate
Mathematics
katieb
  • katieb
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wasiqss
  • wasiqss
evaluate diya LOl
Diyadiya
  • Diyadiya
Equation editor is not working ?
wasiqss
  • wasiqss
it is !

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Diyadiya
  • Diyadiya
Okay integrate -1 to 3/2 |x sin(pi x)| dx
wasiqss
  • wasiqss
ok i will
Diyadiya
  • Diyadiya
tell me how to start
Diyadiya
  • Diyadiya
Equation editor is not working :/
wasiqss
  • wasiqss
ok diya do it by parts i did it
Diyadiya
  • Diyadiya
but there is modulus
wasiqss
  • wasiqss
ohh dint c the modulus
wasiqss
  • wasiqss
w8 tellling u
Diyadiya
  • Diyadiya
okay
Diyadiya
  • Diyadiya
http://ncertbooks.prashanthellina.com/class_12.Mathematics.MathematicsPartII/Integral%20ch_7%2006.11.06.pdf Page number 351 (its written on the top right corner)
wasiqss
  • wasiqss
plz show us how to remove modulus
Diyadiya
  • Diyadiya
full solution is there lol
Diyadiya
  • Diyadiya
i just wanna know that starting part
razor99
  • razor99
ummm guyzzz
Mertsj
  • Mertsj
f=x, f'=dx g'=sin pix g=-1/picospix
Diyadiya
  • Diyadiya
Hm What ? sorry can you explain
Mertsj
  • Mertsj
Do you use u and v or do you use f(x) and g(x) when you integrate by parts.?
Diyadiya
  • Diyadiya
for parts f(x) and g(x)
Mertsj
  • Mertsj
\[f(x)=x\] \[f'(x)=dx\] \[g'(x)=\sin \pi x\] \[g(x)=-\frac{1}{\pi}\cos \pi \]
wasiqss
  • wasiqss
bt man how to remove modulus
Diyadiya
  • Diyadiya
Equation editor isn't working
Diyadiya
  • Diyadiya
Can you see the post @wasiqss
Mertsj
  • Mertsj
I thought you wanted to integrate the function. Didn't know you were trying to remove the modulus.
Diyadiya
  • Diyadiya
Mertsj i cant see what you posted ,it just shows [maths processing error ]
wasiqss
  • wasiqss
diya i can see tho :P
Diyadiya
  • Diyadiya
Wait let me refresh
wasiqss
  • wasiqss
mertsj jus remove the modulus first then i will integrate
Mertsj
  • Mertsj
|dw:1330277056196:dw|
Mertsj
  • Mertsj
Is that the problem or not?
wasiqss
  • wasiqss
yes
Mertsj
  • Mertsj
Then integrate it using the substitutions I gave you.
Diyadiya
  • Diyadiya
|dw:1330277124894:dw|
wasiqss
  • wasiqss
modulus is thea man
Diyadiya
  • Diyadiya
1 Attachment
Mertsj
  • Mertsj
f(x)=x f'(x)=dx g'(x)=sin pi x g(x)= -1/pi cos pi x
Diyadiya
  • Diyadiya
So we dont have to remove modulus first ?
wasiqss
  • wasiqss
yeh diya thats my question
Mertsj
  • Mertsj
Why would you? Integrate the function.
wasiqss
  • wasiqss
mertsj we have do something with modulus first
Mertsj
  • Mertsj
Why?
Diyadiya
  • Diyadiya
This is the solution given in my book
1 Attachment
wasiqss
  • wasiqss
diya this is techniqu for removing modulus that u need to learn from someone cox im not able to recall it
Mertsj
  • Mertsj
Right. Since it's absolute value there are actually two integrals to do.
Mertsj
  • Mertsj
Where was the modulus removed in diyadiya's example post?
Mertsj
  • Mertsj
Which step?
Zarkon
  • Zarkon
find where x sin(pi x) is positive and negative
wasiqss
  • wasiqss
as in how
Mr.Math
  • Mr.Math
Which part of the solution don't you understand Diya?
Diyadiya
  • Diyadiya
the beginning
Mr.Math
  • Mr.Math
Alright. You must know that the definition of absolute value, that's |x|=x, if x>=0 and -x if x<0. So we have to find when \(x\sin(\pi x)\) is positive and when it's negative.
Diyadiya
  • Diyadiya
MrMath i cant see Latex
Mr.Math
  • Mr.Math
Lets first consider the interval from (-1,0). x is obviously negative in this interval, and so is sin(pi*x) because sin(pi x) would lie either in the third or fourth quadrant for x in (-1,0). And hence xsin(pi*x) is the product of two negative number which is positve in (-1,0). Following so far?
Mr.Math
  • Mr.Math
Alright. You must know that the definition of absolute value, that's |x|=x, if x>=0 and -x if x<0. So we have to find when xsin(πx) is positive and when it's negative.
Diyadiya
  • Diyadiya
Why is it in the 3rd or 4th Quadrant ?
Mr.Math
  • Mr.Math
Because when x in (-1,0), the angle, πx in (-π,0), right?
Diyadiya
  • Diyadiya
yeah
Mr.Math
  • Mr.Math
So you know why sin(πx) would be negative in this interval?
Diyadiya
  • Diyadiya
okay sine is negetive in 3rd & 4th Quadrant
Mr.Math
  • Mr.Math
And then the xsin(πx) is positve in (-1,0).
Mr.Math
  • Mr.Math
Now in the interval (0,1) is xsin(πx) positive or negative?
Diyadiya
  • Diyadiya
negative ?
Mr.Math
  • Mr.Math
Lets cut it into two pieces. Is x positive or negative in (0,1)?
Diyadiya
  • Diyadiya
wait a minute , i'm trying to understand the previous thing :D 1min
Mr.Math
  • Mr.Math
Take your time :-)
Diyadiya
  • Diyadiya
Alright
Diyadiya
  • Diyadiya
x is positive in (0,1)
Mr.Math
  • Mr.Math
Good. What about sin(πx)?
Diyadiya
  • Diyadiya
Positive
Mr.Math
  • Mr.Math
Great. So xsin(πx) over all is obviously..?
Diyadiya
  • Diyadiya
positive
Mr.Math
  • Mr.Math
What is the next interval we should consider now?
Diyadiya
  • Diyadiya
(1,3/2) ?
Mr.Math
  • Mr.Math
Right, (1,3/2).
Mr.Math
  • Mr.Math
And xsin(πx) will be positive or negative in this interval?
Diyadiya
  • Diyadiya
positive
Mr.Math
  • Mr.Math
Why?
Diyadiya
  • Diyadiya
hm x is positive in (1,3/2)
Diyadiya
  • Diyadiya
its not ?
Mr.Math
  • Mr.Math
Correct. But what about sin(πx)?
Diyadiya
  • Diyadiya
positive ?
Diyadiya
  • Diyadiya
wait
Diyadiya
  • Diyadiya
No its negative
Diyadiya
  • Diyadiya
since the angle is b/w (pi ,3pi/2)
Mr.Math
  • Mr.Math
Very good. That means that xsin(πx) will be negative in (1,3/2), right?
Diyadiya
  • Diyadiya
Yeah
Mr.Math
  • Mr.Math
So now since you know where our expression is positive and negative you can rewrite it using the definition of absolute value. Can you do that?
Mr.Math
  • Mr.Math
We have found that it's positive in (-1,1) and negative in (1,3/2). You agree?
Diyadiya
  • Diyadiya
why (-1,1) ?
Mr.Math
  • Mr.Math
Didn't we just find that it's positive in (-1,0) and in (0,1)?
Diyadiya
  • Diyadiya
Oh yes !!
Mr.Math
  • Mr.Math
Okay, the next step is to write it as it's written in your book. :-)
Diyadiya
  • Diyadiya
Yeah Got it :D
Diyadiya
  • Diyadiya
Thank You soo much :D that was a great explaination :D
Mr.Math
  • Mr.Math
Awesome!
Diyadiya
  • Diyadiya
Now i can do the rest :-) Thanks again :)
Mr.Math
  • Mr.Math
You're welcome!

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