Post on 15-Jun-2015
Properties Of Definite Integral
Properties Of Definite Integral
b
a
b
a
nn
nxdxx
1 1
1
Properties Of Definite Integral
b
a
b
a
nn
nxdxx
1 1
1
b
a
b
adxxfkdxxkf 2 constantsfactoriseonly can
Properties Of Definite Integral
b
a
b
a
nn
nxdxx
1 1
1
b
a
b
adxxfkdxxkf 2 constantsfactoriseonly can
b
a
b
a
b
adxxgdxxfdxxgxf 3
Properties Of Definite Integral
b
a
b
a
nn
nxdxx
1 1
1
b
a
b
adxxfkdxxkf 2 constantsfactoriseonly can
b
a
b
a
b
adxxgdxxfdxxgxf 3
b
c
c
a
b
adxxfdxxfdxxf 4
b
a
ndxx 0 5
b
a
ndxx 0 5 bxaxf for 0if,
b
a
ndxx 0 5 bxaxf for 0if,
bxaxf for 0if, 0
b
a
ndxx 0 5 bxaxf for 0if,
bxaxf for 0if, 0
b
a
b
adxxgdxxf 6
b
a
ndxx 0 5 bxaxf for 0if,
bxaxf for 0if, 0
b
a
b
adxxgdxxf 6 bxaxgxf for if,
b
a
ndxx 0 5 bxaxf for 0if,
bxaxf for 0if, 0
b
a
b
adxxgdxxf 6 bxaxgxf for if,
a
b
b
adxxfdxxf7
b
a
ndxx 0 5 bxaxf for 0if,
bxaxf for 0if, 0
b
a
b
adxxgdxxf 6 bxaxgxf for if,
a
b
b
adxxfdxxf7
odd is if , 08 xfxfa
a
b
a
ndxx 0 5 bxaxf for 0if,
bxaxf for 0if, 0
b
a
b
adxxgdxxf 6 bxaxgxf for if,
a
b
b
adxxfdxxf7
odd is if , 08 xfxfa
a
even is if , 290
xfxfxfaa
a
b
a
ndxx 0 5 bxaxf for 0if,
bxaxf for 0if, 0
b
a
b
adxxgdxxf 6 bxaxgxf for if,
a
b
b
adxxfdxxf7
odd is if , 08 xfxfa
a
even is if , 290
xfxfxfaa
a
evenevenevenoddevenoddevenoddodd
NOTE
:
e.g. (i) 2
1
26 dxx
e.g. (i) 2
1
26 dxx2
1
3
316
x
e.g. (i) 2
1
26 dxx2
1
3
316
x
14
122 33
e.g. (i) 2
1
26 dxx2
1
3
316
x
14
122 33
5
0
3 dxxii
e.g. (i) 2
1
26 dxx2
1
3
316
x
14
122 33
5
0
31
dxx 5
0
3 dxxii
e.g. (i) 2
1
26 dxx2
1
3
316
x
14
122 33
5
0
31
dxx 5
0
3 dxxii5
0
34
43
x
e.g. (i) 2
1
26 dxx2
1
3
316
x
14
122 33
5
0
31
dxx 5
0
3 dxxii5
0
34
43
x
503
43 xx
e.g. (i) 2
1
26 dxx2
1
3
316
x
14
122 33
5
0
31
dxx 5
0
3 dxxii5
0
34
43
x
503
43 xx
4515
05543
3
3
2
2
5sin xdxiii
function odd function odd 0 5
2
2
5sin xdxiii
function odd function odd 0 5
1
1
23 12 dxxxxiv
2
2
5sin xdxiii
function odd function odd 0 5
1
1
23 12 dxxxxiv
2
2
5sin xdxiii
1
0
2 122 dxx
function odd function odd 0 5
1
1
23 12 dxxxxiv
2
2
5sin xdxiii
1
0
2 122 dxx1
0
3
322
xx
function odd function odd 0 5
1
1
23 12 dxxxxiv
2
2
5sin xdxiii
1
0
2 122 dxx1
0
3
322
xx
310
011322 3
function odd function odd 0 5
1
1
23 12 dxxxxiv
Exercise 11C; 1bce, 2adf, 3ab (i, iii), 4bcf, 5, 6ac, 7df, 8b, 12b, 13*
2
2
5sin xdxiii
1
0
2 122 dxx1
0
3
322
xx
310
011322 3