## Diyadiya Group Title Evaluate 2 years ago 2 years ago

1. wasiqss Group Title

evaluate diya LOl

Equation editor is not working ?

3. wasiqss Group Title

it is !

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

5. wasiqss Group Title

ok i will

tell me how to start

Equation editor is not working :/

8. wasiqss Group Title

ok diya do it by parts i did it

but there is modulus

10. wasiqss Group Title

ohh dint c the modulus

11. wasiqss Group Title

w8 tellling u

okay

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)

14. wasiqss Group Title

plz show us how to remove modulus

full solution is there lol

i just wanna know that starting part

17. razor99 Group Title

ummm guyzzz

18. Mertsj Group Title

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

Hm What ? sorry can you explain

20. Mertsj Group Title

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

for parts f(x) and g(x)

22. Mertsj Group Title

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

23. wasiqss Group Title

bt man how to remove modulus

Equation editor isn't working

Can you see the post @wasiqss

26. Mertsj Group Title

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

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

28. wasiqss Group Title

diya i can see tho :P

Wait let me refresh

30. wasiqss Group Title

mertsj jus remove the modulus first then i will integrate

31. Mertsj Group Title

|dw:1330277056196:dw|

32. Mertsj Group Title

Is that the problem or not?

33. wasiqss Group Title

yes

34. Mertsj Group Title

Then integrate it using the substitutions I gave you.

|dw:1330277124894:dw|

36. wasiqss Group Title

modulus is thea man

38. Mertsj Group Title

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

So we dont have to remove modulus first ?

40. wasiqss Group Title

yeh diya thats my question

41. Mertsj Group Title

Why would you? Integrate the function.

42. wasiqss Group Title

mertsj we have do something with modulus first

43. Mertsj Group Title

Why?

This is the solution given in my book

45. wasiqss Group Title

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

46. Mertsj Group Title

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

47. Mertsj Group Title

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

48. Mertsj Group Title

Which step?

49. Zarkon Group Title

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

50. wasiqss Group Title

as in how

51. Mr.Math Group Title

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

the beginning

53. Mr.Math Group Title

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.

MrMath i cant see Latex

55. Mr.Math Group Title

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?

56. Mr.Math Group Title

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.

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

58. Mr.Math Group Title

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

yeah

60. Mr.Math Group Title

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

okay sine is negetive in 3rd & 4th Quadrant

62. Mr.Math Group Title

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

63. Mr.Math Group Title

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

negative ?

65. Mr.Math Group Title

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

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

67. Mr.Math Group Title

Alright

x is positive in (0,1)

70. Mr.Math Group Title

Positive

72. Mr.Math Group Title

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

positive

74. Mr.Math Group Title

What is the next interval we should consider now?

(1,3/2) ?

76. Mr.Math Group Title

Right, (1,3/2).

77. Mr.Math Group Title

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

positive

79. Mr.Math Group Title

Why?

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

its not ?

82. Mr.Math Group Title

positive ?

wait

No its negative

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

87. Mr.Math Group Title

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

Yeah

89. Mr.Math Group Title

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?

90. Mr.Math Group Title

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

why (-1,1) ?

92. Mr.Math Group Title

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

Oh yes !!

94. Mr.Math Group Title

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

Yeah Got it :D

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

97. Mr.Math Group Title

Awesome!