Evaluate

- Diyadiya

Evaluate

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- wasiqss

evaluate diya LOl

- Diyadiya

Equation editor is not working ?

- wasiqss

it is !

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## More answers

- Diyadiya

Okay integrate -1 to 3/2 |x sin(pi x)| dx

- wasiqss

ok i will

- Diyadiya

tell me how to start

- Diyadiya

Equation editor is not working :/

- wasiqss

ok diya do it by parts i did it

- Diyadiya

but there is modulus

- wasiqss

ohh dint c the modulus

- wasiqss

w8 tellling u

- Diyadiya

okay

- 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

plz show us how to remove modulus

- Diyadiya

full solution is there lol

- Diyadiya

i just wanna know that starting part

- razor99

ummm guyzzz

- Mertsj

f=x, f'=dx g'=sin pix
g=-1/picospix

- Diyadiya

Hm What ? sorry can you explain

- Mertsj

Do you use u and v or do you use f(x) and g(x) when you integrate by parts.?

- Diyadiya

for parts f(x) and g(x)

- Mertsj

\[f(x)=x\]
\[f'(x)=dx\]
\[g'(x)=\sin \pi x\]
\[g(x)=-\frac{1}{\pi}\cos \pi \]

- wasiqss

bt man how to remove modulus

- Diyadiya

Equation editor isn't working

- Diyadiya

Can you see the post @wasiqss

- Mertsj

I thought you wanted to integrate the function. Didn't know you were trying to remove the modulus.

- Diyadiya

Mertsj i cant see what you posted ,it just shows [maths processing error ]

- wasiqss

diya i can see tho :P

- Diyadiya

Wait let me refresh

- wasiqss

mertsj jus remove the modulus first then i will integrate

- Mertsj

|dw:1330277056196:dw|

- Mertsj

Is that the problem or not?

- wasiqss

yes

- Mertsj

Then integrate it using the substitutions I gave you.

- Diyadiya

|dw:1330277124894:dw|

- wasiqss

modulus is thea man

- Diyadiya

##### 1 Attachment

- Mertsj

f(x)=x
f'(x)=dx
g'(x)=sin pi x
g(x)= -1/pi cos pi x

- Diyadiya

So we dont have to remove modulus first ?

- wasiqss

yeh diya thats my question

- Mertsj

Why would you? Integrate the function.

- wasiqss

mertsj we have do something with modulus first

- Mertsj

Why?

- Diyadiya

This is the solution given in my book

##### 1 Attachment

- wasiqss

diya this is techniqu for removing modulus that u need to learn from someone cox im not able to recall it

- Mertsj

Right. Since it's absolute value there are actually two integrals to do.

- Mertsj

Where was the modulus removed in diyadiya's example post?

- Mertsj

Which step?

- Zarkon

find where x sin(pi x) is positive and negative

- wasiqss

as in how

- Mr.Math

Which part of the solution don't you understand Diya?

- Diyadiya

the beginning

- 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

MrMath i cant see Latex

- 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

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

Why is it in the 3rd or 4th Quadrant ?

- Mr.Math

Because when x in (-1,0), the angle, πx in (-π,0), right?

- Diyadiya

yeah

- Mr.Math

So you know why sin(πx) would be negative in this interval?

- Diyadiya

okay sine is negetive in 3rd & 4th Quadrant

- Mr.Math

And then the xsin(πx) is positve in (-1,0).

- Mr.Math

Now in the interval (0,1) is xsin(πx) positive or negative?

- Diyadiya

negative ?

- Mr.Math

Lets cut it into two pieces. Is x positive or negative in (0,1)?

- Diyadiya

wait a minute , i'm trying to understand the previous thing :D
1min

- Mr.Math

Take your time :-)

- Diyadiya

Alright

- Diyadiya

x is positive in (0,1)

- Mr.Math

Good. What about sin(πx)?

- Diyadiya

Positive

- Mr.Math

Great. So xsin(πx) over all is obviously..?

- Diyadiya

positive

- Mr.Math

What is the next interval we should consider now?

- Diyadiya

(1,3/2) ?

- Mr.Math

Right, (1,3/2).

- Mr.Math

And xsin(πx) will be positive or negative in this interval?

- Diyadiya

positive

- Mr.Math

Why?

- Diyadiya

hm x is positive in (1,3/2)

- Diyadiya

its not ?

- Mr.Math

Correct. But what about sin(πx)?

- Diyadiya

positive ?

- Diyadiya

wait

- Diyadiya

No its negative

- Diyadiya

since the angle is b/w (pi ,3pi/2)

- Mr.Math

Very good. That means that xsin(πx) will be negative in (1,3/2), right?

- Diyadiya

Yeah

- 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

We have found that it's positive in (-1,1) and negative in (1,3/2). You agree?

- Diyadiya

why (-1,1) ?

- Mr.Math

Didn't we just find that it's positive in (-1,0) and in (0,1)?

- Diyadiya

Oh yes !!

- Mr.Math

Okay, the next step is to write it as it's written in your book. :-)

- Diyadiya

Yeah Got it :D

- Diyadiya

Thank You soo much :D that was a great explaination :D

- Mr.Math

Awesome!

- Diyadiya

Now i can do the rest :-)
Thanks again :)

- Mr.Math

You're welcome!

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