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VED1
          E\L-LOVELY-H\math16-1 IInd 6-8-11 IVth 21-4-12 Vth 20-8-12 Vth 20-8-12 VIth 10-9-12



          vFkZ'kkfL=k;ksa dk xf.kr




                   uksV
                                                  1



                                  8-  ljy js[kk   ,  a  }kjk foHkkftr o`Ùk    0    ,    osQ Hkkxksa osQ {ks=kiQyksa dk vuqikr Kkr dhft,A
                                                  2
                                      ¹laosQr% vHkh"V Hkkxksa osQ {ks=kiQyksa dk vuqikr eku yhft,   ,   
 
 θº-
                                                                  ,  ∫  a a /2  y dx  : ∫  − a a /2 y dx



                                                                               2
                                                                                                2
                                                                  ,  ∫  a a /2  a −  2  x dx  : ∫  − a a /2  a −  2  x dx

                                                                     mÙkj
                                                                                                 56

                                         2                                      π oxZ bdkbZ !        oxZ bdkbZ
                                                                                                  5
                                         1                                     2    b          1   b 2
                                  4-  73    oxZ bdkbZ                       5- b    log    6-      e   − 1   
                                         15                                         a          2
                                      9
                                  7-    m  oxZ bdkbZ                        8- (4π− 3 3) : (8π+  3 3)
                                      2
                                Lo&ewY;kadu


                                1- fjDr LFkkuksa dh iwfrZ djsa  *     
  +     
:
 µ
                                                                        ---------
                                         vktdy lekdyu dk iz;ksx vFkZ'kkL=k esa    ls c<+k gSA
                                                          ---------
                                         fuf'pr lekdyu ,d      lhek gSA
                                                    ---------
                                      !  miHkksDrk cpr    fof/ ls Kkr fd;k tk ldrk gSA
                                16-2 vFkZ'kkL=k esa lekdyu dk mi;ksx



                                      vktdy lekdyu dk iz;ksx vFkZ'kkL=k esa rsth ls c<+k gSA bls ge fuEufyf[kr rF;ksa ls Li"V dj ldrs
                                gSaµ
                                      1- lhekUr ykxr] vkSlr ykxr rFkk oqQy ykxr

                                                                     ()
                                                                    dc
                                                   pw¡fd lhekUr ykxr ,   gksrk gS] vr%
                                                                     dq
                                                                       ()
                                                          oqQy ykxr ,  ∫  dc  . dq
                                                                      dq
                                          dc
                                            ()
                                      ;gk¡]    , lhekUr ykxr]   , oqQy ykxr]    , mRiknu esa ifjorZuA
                                           dq
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