Techniques for Integration Indefinite integral : text s.t.F.IN = fix ) FK1 = [ fltldt ovger closed interval La , × ] ; - continuous Since the derivative of a constant function is Zero , we have { fat dx = Flx ) + 0 , E is constant Methedofsubstitutionf fix ) dx = f. F' 4) dx = FLXI + I set × = gltl = Fight ) ) + 0 = / If Flglttldt = IF 'lgItI)g' ltldt = / fight ) ) gtltldt
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FK1 = [ fltldt ovger closed interval La , × ] ;
- continuous
,
E is constant
Methedofsubstitutionffix) dx = f. F'4) dx = FLXI + I set × = gltl = Fight) ) + 0 = / If Flglttldt = IF'lgItI)g' ltldt = / fight) ) gtltldt
Y =fix)
Except I ¥g , a > 0
Let x= at ; dx= adt
1±÷-- I = I :# = ¥aTctant + C'
= Earthen # to
× = at ⇒ a = at ⇒ t = Ha
p = at ⇒ t - Pla B Ma
!±÷=±aI±Et I %
= ( arttan ? - arttan 1)
×
> 0
o o
= ¥ IT a2
Identities :
a
- continuous
,
E is constant
Methedofsubstitutionffix) dx = f. F'4) dx = FLXI + I set × = gltl = Fight) ) + 0 = / If Flglttldt = IF'lgItI)g' ltldt = / fight) ) gtltldt
Y =fix)
Except I ¥g , a > 0
Let x= at ; dx= adt
1±÷-- I = I :# = ¥aTctant + C'
= Earthen # to
× = at ⇒ a = at ⇒ t = Ha
p = at ⇒ t - Pla B Ma
!±÷=±aI±Et I %
= ( arttan ? - arttan 1)
×
> 0
o o
= ¥ IT a2
Identities :
a
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