# The value of `int_(-pi//2)^(pi//2)[ cot^(-1)x] dx` (where ,[.] denotes greatest integer function) is equal to

Updated On: 8-5-2021

6.5 k+

4.7 k+

Answer

Text Solution

(a)

pi+ cot 1

(b)

pi+ cot 2

(c)

pi+ cot1 + cot2

(d)

cot 1+cot 2

C

Transcript

Time | Transcript |
---|---|

00:00 - 00:59 | hello student today occasion is the value of integration minus 5 by 2 2 pi by 2 Cos inverse x dx where this represent denotes a greatest integer function is equals to a b c d option is given software to find which option is correct so we can write our integration function let it is equals to + 22 + 5 by 2 and this is greatest integer function of cot inverse X into DX and let ise equal to minus 5 by 2 and here is pi by 2 greatest integer function cot inverse X into DX so on adding this we get to Y is equals to integration minus 5 by 2 |

01:00 - 01:59 | 2 + 5 by 2 into cot inverse minus x here we have to write Pi -2 take protein versus negative so we can write it by minus this is a minus cot inverse x as we have to take negative value of cot inverse so this is cot inverse X greatest integer function minus minus cot inverse X into DX ear so this isn't complete DX sunao from here we can write 2 Y is equals to 2 time of sevitech to outside the integration so this is pi by 2 minus 5 by 2 so we can write a cot inverse x |

02:00 - 02:59 | minus minus will become + + cot inverse x minus 5 and the season on the exterior so from here we can write is equals to 2 and 2 will be cancel out Yeh 0 to pi by 2022 into cot inverse X + this can be written as ko theta minus 5 minus cot inverse is also equal to this so this is cot inverse into DX so this will cause 2022 and here we have cot inverse X into DX + we can separate the |

03:00 - 03:59 | these 0 to pi by 2 into 1 minus cot inverse X into DX so on solving this we get it is equals to our eyes equals to firstly with take this part 20 to 22 Court inverse X into DX from here we can write Court inverse pi by 2 or 3 verse 5 by 2 is equals to X and now from here we can write Court pi by 2 is equals to multiply with quote so we get cortex hair or we can simplify this quote x is equal to pi by 2 from here we get covid-19 -1 so we can write a |

04:00 - 04:59 | covid-19 ko tax is equal to covid-19 is one so we can write this is 1 and X is equals to 1 we get i0 here is integration 0 we get 0281 into one into DX and + cot 1 up to pi by 2 and here is zero 2dx so this will equals to covid-19 from here we can write h i 1 is equals to integration is equals to integration 0 to pi by 2 minus cot inverse |

05:00 - 05:59 | into DX share from here we can write 5 - 2 x 25 and we get two values of cot inverse as 1.54 and 3.4 so this is 3.4 abhi ke naye dance subtract the values of we get similar values for this is 3.4 - 2 so from here we get Pi minus cot inverse X is equals to 1 and from here we get by minus cot inverse X is equals to 2 from here we can write Pi minus cot inverse X is equals to 2 x 2 - 2 |

06:00 - 06:59 | is equals to Cos inverse X share so from here we can write X is equals to court as we have multiplied with quote here only accept accept air and code 52 from here we get access to codepipeline Scott to so now we can write integration 1 is equals to integration 0 2 - CO2 and here is 1 into X + this is minus cot Tu To Pi by 2 and this is 2 into DX so from where we get this is equal to minus cot 2 and this will equals to |

07:00 - 07:59 | 2.22.2 so this will equals to minus root 2 + 5 so this is our I one know we can write IGI sequels 20 + 1 and we have calculated as low as Court one so we can write your quote one where is + 2 into court to also and from here we get to go to and this is equal to pi plus covid-19 from my zero is our Court to be have zero is covid-19 this is Court to hear so we can I got one + 5 + CO2 and we can write this as our integration function is equals to 5 + 1 + cot |

08:00 - 08:59 | so this is the answer so we check which option is correct option C is correct Pi Court oneplus ko to so this is the answer thank you |

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