JEE  >  Important Formulas: Definite Integrals

# Important Formulas: Definite Integrals - Mathematics (Maths) for JEE Main & Advanced

``` Page 1

Page # 17
DEFINITE INTEGRA TION
Properties of definite integral
1.
?
b
a
) x ( f dx =
?
b
a
) t ( f dt 2.
?
b
a
) x ( f
dx = –
?
a
b
) x ( f
dx
3.
?
b
a
) x ( f
dx =
?
c
a
) x ( f dx +
?
b
c
) x ( f dx
4.
?
?
a
a
) x ( f dx  =
?
? ?
a
0
)) x ( f ) x ( f (
dx  =
?
?
?
?
?
?
?
?
)x ( f – )x (– f , 0
)x ( f ) x (– f , dx )x ( f 2
a
0
5.
?
b
a
) x ( f dx  =
?
? ?
b
a
) x b a ( f dx
Page 2

Page # 17
DEFINITE INTEGRA TION
Properties of definite integral
1.
?
b
a
) x ( f dx =
?
b
a
) t ( f dt 2.
?
b
a
) x ( f
dx = –
?
a
b
) x ( f
dx
3.
?
b
a
) x ( f
dx =
?
c
a
) x ( f dx +
?
b
c
) x ( f dx
4.
?
?
a
a
) x ( f dx  =
?
? ?
a
0
)) x ( f ) x ( f (
dx  =
?
?
?
?
?
?
?
?
)x ( f – )x (– f , 0
)x ( f ) x (– f , dx )x ( f 2
a
0
5.
?
b
a
) x ( f dx  =
?
? ?
b
a
) x b a ( f dx
Page # 18
6.
?
a
0
) x ( f dx =
?
?
a
0
) x a ( f dx
7.
?
a 2
0
) x ( f
dx  =
?
? ?
a
0
)) x a 2 (f ) x (f ( dx  =
?
?
?
?
?
?
?
?
) x (f – ) x – a 2 (f , 0
)x ( f )x – a 2 ( f , dx )x ( f 2
a
0
8.  If f(x) is a periodic function with period T, then

?
nT
0
) x ( f dx  = n
?
T
0
) x ( f dx, n ? z,
?
?nT a
a
) x ( f dx  = n
?
T
0
) x ( f dx, n ? z, a ? R

?
nT
mT
) x ( f dx  = (n – m)
?
T
0
) x ( f dx, m, n ? z,
?
?nT a
nT
) x ( f dx  =
?
a
0
) x ( f dx, n ? z, a ? R
?
?
?
nT b
nT a
) x ( f dx  =
?
a
a
) x ( f dx, n ? z, a, b ? R
9.     If ?(x) ? f(x) ? ? (x) for a ? x ? b,
then
?
?
b
a
) x (
dx  ?
?
b
a
) x ( f
dx ?
?
?
b
a
) x ( dx
10.  If m ? f(x) ? M for a ? x ? b, then m (b – a) ?
?
b
a
) x ( f dx ? M (b – a)
11.  If f(x) ? 0 on [a, b] then
?
b
a
dx ) x ( f ? 0
Leibnitz Theorem :   If F(x) =
?
) x ( h
) x ( g
dt )t (f , then
dx
) x ( dF
= h ?(x) f(h(x)) – g ?(x) f(g(x))
```

## Mathematics (Maths) for JEE Main & Advanced

129 videos|408 docs|306 tests

## Mathematics (Maths) for JEE Main & Advanced

129 videos|408 docs|306 tests

### Up next

 Explore Courses for JEE exam
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Track your progress, build streaks, highlight & save important lessons and more!
Related Searches

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;