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JEE Mains 2021: King’s Property + Byparts | Definite Integration | 2 Approaches Explained | JEE PYQs
JEE Mains 2021: King’s Property + Byparts | Definite Integration | 2 Approaches Explained | JEE PYQs | JEE 2025
In this video, I have discussed a JEE Mains 2021 question from definite integration, which combines the concepts of King’s Property and Byparts. To help you understand better, I have solved this problem using two different approaches-each offering unique insights and tricks to tackle such questions effectively.
This is a must-watch for JEE Mains 2025 and 2026 aspirants to strengthen their definite integration skills. Make sure to watch the full video to learn both methods and choose the one that suits you best!
Don’t forget to subscribe to Factorial Academy and enable notifications to stay updated with more conceptual and exam-focused videos.
#jee2025 #jeeadvanced2025 #jeepyqs #maths
#jeemains2021 #definiteintegration #kingsproperty #integrationbyparts #jeepreparation #jeemains2025 #jeemains2026 #factorialacademy #jeeconcepts #iitjee #jeemath
มุมมอง: 478

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ความคิดเห็น

  • @MEBMohdSaifuddinKhan
    @MEBMohdSaifuddinKhan 3 ชั่วโมงที่ผ่านมา

    An easier solution is to make the limits variable using the substitution x-t=k and then use the lebinitz formula and use maxima minima concept.

  • @abdulreyhan9760
    @abdulreyhan9760 6 ชั่วโมงที่ผ่านมา

    Beautifully explained at every point..❤❤❤.

  • @kotakikahanik
    @kotakikahanik 6 ชั่วโมงที่ผ่านมา

    Sir eek pyqs hai x+2y+3z=42 , jee mains 2024 ka 1 Feb , plzz wo karwa dijiye , uska net par soln kafi lengthy hai

    • @Rudrubro11
      @Rudrubro11 6 ชั่วโมงที่ผ่านมา

      +1

  • @manavkumar8235
    @manavkumar8235 8 ชั่วโมงที่ผ่านมา

    Sir ek question joh topic aap batate hai waisa sa hii ek question extra leke aaya kariye and usko as home work de Diya kariye

  • @darshilmahajan5551
    @darshilmahajan5551 8 ชั่วโมงที่ผ่านมา

    Pnc n probability plz

  • @darshilmahajan5551
    @darshilmahajan5551 8 ชั่วโมงที่ผ่านมา

    Sir ek saath zyada ques laiye plz

  • @aravpratap61
    @aravpratap61 9 ชั่วโมงที่ผ่านมา

    the question framing is crazy

  • @johanliebert-ny6pk
    @johanliebert-ny6pk 15 ชั่วโมงที่ผ่านมา

    phle maine socha tha ki Identity bna ke fn nikl lu then solve karu but nhi hua

  • @johanliebert-ny6pk
    @johanliebert-ny6pk 15 ชั่วโมงที่ผ่านมา

    what an amazing soln

  • @AdityaKumar-y1l3t
    @AdityaKumar-y1l3t 15 ชั่วโมงที่ผ่านมา

    Exam me aise hi q maths ke percentile increase karte

  • @manavkumar8235
    @manavkumar8235 17 ชั่วโมงที่ผ่านมา

    Very clever approach in solving inequality Thanks sir

  • @masterchief-d1z
    @masterchief-d1z วันที่ผ่านมา

    sir please pnc ke questions

  • @Harshit-r7m
    @Harshit-r7m วันที่ผ่านมา

    can be more quick 2/3 of rectangle

    • @aniruddhgehlot
      @aniruddhgehlot 11 ชั่วโมงที่ผ่านมา

      I also thought the same, the breadth will be 4 but what about the length?

    • @shubhampratapsingh3041
      @shubhampratapsingh3041 8 ชั่วโมงที่ผ่านมา

      ​@@aniruddhgehlot Length will be 8

  • @aparna2144
    @aparna2144 วันที่ผ่านมา

    Nice

  • @kotakikahanik
    @kotakikahanik วันที่ผ่านมา

    Thank you sir really helpful ❤

  • @tastron9991
    @tastron9991 วันที่ผ่านมา

    Sir iske ke andar ek aur idea hain, [x²] ka integration from 0 to some constant lene mein √2,√3 karke saare radicals aayenge and tthey cant be eliminated so alpha ki value iss format mein 2 hi hogi.

  • @lakshayraj2939
    @lakshayraj2939 2 วันที่ผ่านมา

    i am still worthy😅..

  • @srvgaming6588
    @srvgaming6588 2 วันที่ผ่านมา

    Amazing video sir loved it ❤️

  • @Dhaneesh_7
    @Dhaneesh_7 2 วันที่ผ่านมา

    Stuck in remembering the formula 😤

    • @factorialacademy
      @factorialacademy วันที่ผ่านมา

      Shortest distance formula is important

    • @Dhaneesh_7
      @Dhaneesh_7 วันที่ผ่านมา

      @factorialacademy yaad agya tha baad me sir

  • @Deevige
    @Deevige 2 วันที่ผ่านมา

    The question is unnecessarily lengthy, combining concepts from 3D geometry, integration, and the greatest integer function. It feels like an exercise in pure labor rather than testing genuine knowledge. The amount of time required to solve it is excessive, and the level of conceptual understanding needed is minimal. The question seems to prioritize complexity and calculation over testing deep understanding or problem-solving skills for jee But once again your teaching is excellent My 🫡 salutes to ur knowledge and inspiration and teaching sir

    • @riteshjadhav3984
      @riteshjadhav3984 2 วันที่ผ่านมา

      Unnecessary lengthy

    • @OmPrakash-pc1ec
      @OmPrakash-pc1ec 2 วันที่ผ่านมา

      half of recent jee maths right there😊

    • @tmrapper6378
      @tmrapper6378 2 วันที่ผ่านมา

      Most sane jee aspirant

    • @factorialacademy
      @factorialacademy วันที่ผ่านมา

      Yes it’s lengthy

    • @atulyaroy8962
      @atulyaroy8962 วันที่ผ่านมา

      I mean this ain't jee advanced

  • @jeemain2025-i5e
    @jeemain2025-i5e 2 วันที่ผ่านมา

    😃

  • @Vabadrish
    @Vabadrish 3 วันที่ผ่านมา

    A fster method would be to notice that g(x).ln part is an even function Integrating an even function(definite integration) give odd function Thus f(x) is odd and integrate f(x) gives 0

    • @rankpolin2287
      @rankpolin2287 2 วันที่ผ่านมา

      A much faster method would be to know somehow f(x) would have to be zero as can't intrgrate without it to get a value😂.. And assuming that integrare the 2nd part and find the answer

    • @rankpolin2287
      @rankpolin2287 2 วันที่ผ่านมา

      Also g(x) is odd its given... Why will we assume it to be even😅

    • @Vabadrish
      @Vabadrish 2 วันที่ผ่านมา

      @@rankpolin2287 ln(1-t/1+t) is odd and g(x) is odd Multiplying two odd functions, we get an even function Aur mainebhi aise hi under 4 min solve Kiya tha ye assume karke ki f(x) ka integration zero hoga 🤣🙏

    • @dazzlekazzle
      @dazzlekazzle 2 วันที่ผ่านมา

      is integrating an even function always supposed to give us an odd funcn?

    • @Vabadrish
      @Vabadrish 2 วันที่ผ่านมา

      @@dazzlekazzle if you don't take the integration constant...which ofc will not come if you integrate from a to x such that f(a)=0

  • @vedantgg7084
    @vedantgg7084 3 วันที่ผ่านมา

    Ek do hw bhi dediya kro sir

    • @tanujsharma8026
      @tanujsharma8026 3 วันที่ผ่านมา

      Yes sirr please

    • @factorialacademy
      @factorialacademy วันที่ผ่านมา

      Ok will include HW questions

    • @vedantgg7084
      @vedantgg7084 วันที่ผ่านมา

      @@factorialacademy thanks sir

  • @Deevige
    @Deevige 3 วันที่ผ่านมา

    What an amazing method of solving sir thanks

  • @AlokRaj-c1f
    @AlokRaj-c1f 3 วันที่ผ่านมา

    Thank you sir for discussing best question of jm

  • @Cooososoo
    @Cooososoo 3 วันที่ผ่านมา

    WHAT about x=0 ? It is also a root

    • @Yeah_its_desi
      @Yeah_its_desi 3 วันที่ผ่านมา

      Count kia to hai usse

    • @Cooososoo
      @Cooososoo 3 วันที่ผ่านมา

      @Yeah_its_desi kaise?

    • @SPIDERGAMING2505
      @SPIDERGAMING2505 3 วันที่ผ่านมา

      ​@@Cooososoobhai y²= x me (0,0 ) hota he ki nhi hota ha na vaise hi 0,0 ko count Kiya ha

  • @mokshjain7403
    @mokshjain7403 3 วันที่ผ่านมา

    Ye question olympiad se utha hai

  • @helpmepls282
    @helpmepls282 3 วันที่ผ่านมา

    Thanks sir, could you take up this one question of quadratic equations from SEPTEMBER 21ST 2021 jee mains ( the number of pairs (a,b) ........ )

  • @itskrish2911
    @itskrish2911 3 วันที่ผ่านมา

    Sir please evaluate this question Let f : ( − ∞ , ∞ ) − { 0 } → R f : ( − ∞ , ∞ ) − { 0 } → R be a differentiable function such that f ′ ( 1 ) = lim a → ∞ a ^2 f ( 1 /a ) . Then lim a → ∞ a ( a + 1 )/2 tan^− 1 ( 1/a ) + a^2 − 2 log e a is equal to

  • @SPIDERGAMING2505
    @SPIDERGAMING2505 3 วันที่ผ่านมา

    Cartesian graph par plot kar ke kiya tha yeh question

  • @kotakikahanik
    @kotakikahanik 3 วันที่ผ่านมา

    Sir please matrices + pnc Wale ques pe video plzzzz 🙏🙏

    • @factorialacademy
      @factorialacademy วันที่ผ่านมา

      Here it is th-cam.com/video/3emfFyDA1vk/w-d-xo.htmlsi=ocudlpmHrhm5WICm

  • @chiragmalhotra6312
    @chiragmalhotra6312 3 วันที่ผ่านมา

    Complex no. Meets geometry meets sets meets inequality 🎉😂

  • @Yasir-Ali1
    @Yasir-Ali1 4 วันที่ผ่านมา

    👍

  • @rishabhtiwari2325
    @rishabhtiwari2325 4 วันที่ผ่านมา

    First time i did this question in definite integration class test i just assumed that f will be odd without working that part out luckily i was saved. 😅

    • @RC24India
      @RC24India 4 วันที่ผ่านมา

      I did the same. But it was quite obvious if you observe it.

    • @AdityaKumar-y1l3t
      @AdityaKumar-y1l3t 2 วันที่ผ่านมา

      Yes i also did the same

  • @rahulsachdeva4046
    @rahulsachdeva4046 4 วันที่ผ่านมา

    Good question

  • @rahulsachdeva4046
    @rahulsachdeva4046 4 วันที่ผ่านมา

    👌🏻

  • @rahulsachdeva4046
    @rahulsachdeva4046 4 วันที่ผ่านมา

    Love your consistency. Way to go❤

    • @rishabhtiwari2325
      @rishabhtiwari2325 4 วันที่ผ่านมา

      Kohli is also very consistent 😂

  • @CubeRex_
    @CubeRex_ 4 วันที่ผ่านมา

    Ez in 2 mins

    • @mekohai4458
      @mekohai4458 3 วันที่ผ่านมา

      U mean gave up in 2 mins ezz??😂😂

  • @HimanshuSoni-c3y
    @HimanshuSoni-c3y 4 วันที่ผ่านมา

    Those 100k from 2.6k will come soon💫

    • @factorialacademy
      @factorialacademy วันที่ผ่านมา

      Thankyou so much! Stay connected..

  • @somuapti
    @somuapti 4 วันที่ผ่านมา

    Super solution. I am a senior JEE Maths faculty.

  • @Soulofindia111
    @Soulofindia111 4 วันที่ผ่านมา

    Sir ...why did you conclude that modulus will open according to value of x?

    • @itachi3625
      @itachi3625 4 วันที่ผ่านมา

      Beacuse integral is function with t as the variable. Its given that t will lie between 0-2 so opening modulus depends on value of x which isn't known.

  • @iamyatharthh
    @iamyatharthh 4 วันที่ผ่านมา

    Fucking Good problem!💀

  • @earthisflatandiamapenguin.5995
    @earthisflatandiamapenguin.5995 4 วันที่ผ่านมา

    sir, f(x)= 0 to 2 int e^|x-t| dt, isme agar x=t put kare, f(t)= 0 to 2 e^0dt =2 hua minimum?

  • @maulikshah28
    @maulikshah28 4 วันที่ผ่านมา

    amazing

  • @tyagisuman1934
    @tyagisuman1934 4 วันที่ผ่านมา

    Absolutely helpful ...👍

  • @Deevige
    @Deevige 4 วันที่ผ่านมา

    Respected Sir can we do like this When the value of x is greater than 2, the function behaves in such a way that it equals a shifted version of itself. As x increases, the curve continues to rise above a certain point, indicating that the curve has a maximum value and then starts to fall as you move further to the right of x equals 2. On the other hand, when x is less than 0, the curve starts from negative infinity and rises up to a specific point. This shows that the curve has maximum values at both ends, specifically at x equals 0 and x equals 2. Therefore, these points are maximum points, not minimum ones. Now, between the range of 0 < x < t where t is less than 2, there should be one point where the two parts of the function intersect. The function takes two forms: one decreases and the other increases, and they can only be equal when x and t are both equal to 1. Taking into account the symmetry of the function, you would integrate a certain expression, and the result of that integration So it is twice of integration between zero and 2 of e power 1 -t with respect to t Sir this gives the final answer as twice the difference between the constant e and 1.

  • @doge_the_cat
    @doge_the_cat 4 วันที่ผ่านมา

    For minima always symmetry is obtained so make graph symmetrical about x = 1 and double the integral of e^x from 0 to 1 oral answer 2(e-1)

  • @JeeAsprirant22
    @JeeAsprirant22 4 วันที่ผ่านมา

    We really need such channels which can provide Good solutions to pyqs .Thank you so much sir.

    • @factorialacademy
      @factorialacademy วันที่ผ่านมา

      You're welcome! Stay connected, keep learning.

  • @lakshayraj2939
    @lakshayraj2939 5 วันที่ผ่านมา

    keep it up 😊

  • @SeriousAspirantJEE
    @SeriousAspirantJEE 5 วันที่ผ่านมา

    What a beauty ❤️❤️