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INDEFINITE INTEGRATION iff & F ave fonction of x such thet Fé) = fd then the bmoction F & Sal a PREMITIVE OR ANTIDERIVATIVE OR INTEGRAL of fk) wrt x ani s witen aeboboly os [ide = Foy sce St) seis ffx). where c is ceBed the constant of inbegretion. GEOMETRICAL INTERPRETATIGN OF INDEFINITE ENTEGRAL =: [totes = Fod + ¢ = visev)_ represents a betly of cows. The @fferent veles of c will comespond to different members of this family and these members can be oit@ined ty dkifing any one of the curves parallel to itself, This is the geometrical interpretation of indefiete Extearel Let fh) = Be. Then J flckdy = x? +c. For ciferent velses of c. we get different intedreb. Hut these infere’s =e very similar qeometricalhy. Thos, y = 0+ c where c 6 arbiters coment represents a family of integrais. By asieting GHiaent webs tc awe get different members of the fousty. These together constitute the indefinite iteqrel In this case, each istazel represents a parabola with # acs slong yexds. # the Ene x = a intersects the parebobs y = x7 v = 2 =], gests 2 ysx'-Lyss'-2aP PPL PL Pes x respectively, then = at these potas apes Da This indicates that the tangents to the ave: af these points are parallel. Thus, faxdeex*+c=fxlee tsa), impligs that the tanger to all the cove: ffx) +c, c & RB, at the points of Estesection of the curves by the ine x = 2, fa © RB), ore parelie! STANDARD RESULTS = faxcebpt & 21 a face bfx = een ed a Jose etnlese lee 7 m-g ta} fetta = 2 +c {is} forte =? +c {a>} a p fna 1 1 iv} Jeter e bys = ~—coster +b) (4 Jeostax + bx =Ssintax +b) + ten} Jrantax ¢ bide = 2 en soefax +2)1 +e (a) Joovax + byte = 14m) cmntax +t) +e a a (isp fece*tae + bei = Atentex +b} sc fe} eorectex e bite = —Leottax tb} +c a 2 ta} Jeosectax +b}.cotfax + bide = = cosee (ax sblec 2 i fx) Jocc ex + bhtanfaer + bik = eedar tb} re 
