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Time | Transcript |
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00:00 - 00:59 | hello students today aur question is if integration 0 2 X greatest integer function of X into DX is equal to zero to greatest integer function of X Into X into DX where are you doesn't belong 20 where this and this is not the greatest integer function and fractional part of the respectively then the value of 4 into fractional part of X is equals to so we have to find this so we can write a integration 0 2x and greatest integer function of X is equals to we can write here this is 0 to 10 X + 12 2nd year arts and here we have taken x0x one and their access to 23 so be taken to into DX and this is |

01:00 - 01:59 | new aap to x minus 1 and here is X so we get x minus 1 year so we get x minus 1 into DX so now we can write we can write integration of integration of x to DX is equal to zero 2 by taking right and this side of by taking this is our elders this is Rs so this will zero to greatest integer function X Into X into DX so this will = 2 x square x square divided by x divided by 2 |

02:00 - 02:59 | and here is greatest integer function X and Y = 2 dismil = 2 greatest integer function of x power 2 and this is divided by 2 minus zero from here we get greatest integer function square divided by these all times are equal so from here we can write one plus DL 20 plus one plus into minus 1 into 2 - 1 + 2 into 3 - 2 + 3 into 4 - 3 and this is continue up to |

03:00 - 03:59 | greatest integer function X here is greatest integer function x minus greatest integer function of X is equals to greatest integer function of x square - 2 year is greatest integer function and this is my plus one here as in all terms we added so that this is + 8 so we can write it as X + 1 - greatest integer function of X is equals to greatest integer function of x square divided by 2 from here we can ride 123 this is information 123 and this is up to x minus 1 equals to greatest integer function of x square |

04:00 - 04:59 | Tu so from here we know that some of the natural numbers is equals to and into an + 1 divided by 2 from here we can write X this is our hand and hour access the greatest integer function of 2 - + greatest integer function of X into fractional part of X and this will cause 2 x square divided by 2 from here by taking this function greatest integer function common so we get X + 1 + X and this is divided by 2 this is fractional part and this is equals to greatest integer function square - / to so this will cancel out here so we left will greatest integer function this is minus 9 plus so we can |

05:00 - 05:59 | corrected so this is my Naseer from here we get -6 greatest integer function of 1 -2 and fractional part of x = 2 X this is a greatest integer function so this will / to so on solving this we get by taking to as LCM so we get greatest integer function - 2 + 2 time of fractional part and this will cause 2x and two and two will be cancel out here now we get greatest integer function is also cancel out so we get -1 this will cancel out so fractional X is equals to zero from here to time of X is equals to 1 |

06:00 - 06:59 | so from here we can ride for time of the time of greatest integer function is equals to 2 into 1 2 decimal = 22 so this is our answer thank you |