Odd & Even Functions

(1) Even f x f x

a a

f x dx 2 f x dx

a 0

Odd & Even Functions

(1) Even f x f x

a a

f x dx 2 f x dx

a 0

ca ca

NOTE: horizontal shift

f x c dx 2 f x c dx

ca c

Odd & Even Functions

(1) Even f x f x

a a

f x dx 2 f x dx

a 0

ca ca

NOTE: horizontal shift

f x c dx 2 f x c dx

ca c

(2) Odd f x f x

Odd & Even Functions

(1) Even f x f x

a a

f x dx 2 f x dx

a 0

ca ca

NOTE: horizontal shift

f x c dx 2 f x c dx

ca c

(2) Odd f x f x

a

f x dx 0

a

Odd & Even Functions

(1) Even f x f x

a a

f x dx 2 f x dx

a 0

ca ca

NOTE: horizontal shift

f x c dx 2 f x c dx

ca c

(2) Odd f x f x

a

f x dx 0

a

ca

NOTE: horizontal shift

f x c dx 0

ca

Odd & Even Functions

(1) Even f x f x

a a

f x dx 2 f x dx

a 0

ca ca

NOTE: horizontal shift

f x c dx 2 f x c dx

ca c

(2) Odd f x f x

a

f x dx 0

a

ca

NOTE: horizontal shift

f x c dx 0

ca

a a

f x dx f a x dx

(3)

0 0