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VED1
E L-LOVELY-H math12-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

noEPk;soh dk rfDs

B'N • fuzBQ “ ” nB[ebB dk gqshe j? fi;B{z nB[ebB fuzBQ (sign of integration) efjzd/

jB. fJj cbB d/ nB[ebB B{z do;kT[Adk j?. dx ftZu x d[nkok fJj gqrN j[zdk j? fe
nB[ebB (integration) uo (variable) x d/ ;kg/y ehsk frnk j?.
• fe;h cbB dk eqw nB[;ko nB[ebB ns/ fBy/VB d'B'A fefonktK fdZsh ikD sK cbB
T[;h soQK ofjzdk j?.
• fe;h cbB dk nB[ebB ftbZyD (unique) BjhA j[zdk, feT[Ai' c B{z fGzB^fGzB wkB d/D s/
F(x) d/ eJh nB[ebB (integrals) gqkgs j[zd/ jB, fJ; soQK i/eo f (x), F (x) dk e'Jh
nB[ebB (intregal) j't/, sK f (x) + c T[;dk ftnkge nB[ebB (Comprehensive
Integral) j't/rk.

12H7 Ppde'P (Keywords)

• gqshb'w (Inverse) ^ T[bNk.
• gqshe (Symbol) ^ fuzBQ.

12H8 nfGnk; gqPB (Review Questions)

1H dk x d/ ;kg/y nB[ebB gsk eo', fiZE/ (T[Zso L ),

2H nB[ebB dk wkB gsk eo'. (T[Zso L e x + c)

3H dk wkB gsk eo'. (T[Zso L –6 cos x + c)

4H dk wkB eZY'. (T[Zso L )

5H dk wkB gfoefbs eo'. (T[Zso L tan x – x + c)

T[Zso L ;t?^w[bKeD (Answer: Self Assessment)

1H nB[ebB 2H nB[ebe 3H 4H sin x 5. n + 1.

6H ;Zu 7H M{m 8H ;Zu 9H ;Zu.

12H9 ;zdoG g[;seK (Further Readings)

p[e;
1H w?E/w/fNe; cko fJe'B'fw;N ^ f;w'B ns/ pb{w, thtk gpfbe/PB.
2H w?E/w/fNe; cko fJe'B'fw;N ^ :kwkB/, gq?AfN; jkb fJzvhnk.
3H w?E/w/fNe; cko fJe'B'fw;N ^ w/jsk ns/ wdBkBh, ;[bskB uzd n?Av ;z;.
4H J;/AfPnb w?E/w/fNe; cko fJe'B'fwe; ^ B'N ;/v/;No, ghNo jkwzv, gq?AfN; jkb
gpfbH.
5H w?E/w/fNe; cko fJe'B'fwe; ^ wkbe'w, fBe'b;, :{H;hH bzdB.
6H noEPk;soh dk rfDs ^ wkJheb j?oh;B, g?fNqe tkbvoB.
7H w?E/w/fNe; cko fJe'B'fwe; ^ ekob ghH f;w'B, b'o/A; pb{w.
8H w?E/w/fNe; cko fJe'B'fwe; n?Av ckJhBK; ^ wkofNB BkowB.
9H w?E/w/fNe; cko fJe'B'fwe; ^ ekT{Af;b cko fJe'B'fwe n?i{e/PB.

194 LOVELY PROFESSIONAL UNIVERSITY