TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
X2 t04 08 odd & even functions (2012)
1. Odd & Even Functions
(1) Even f x f x
2. Odd & Even Functions
(1) Even f x f x
a a
f x dx 2 f x dx
a 0
3. 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
4. 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
5. 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
6. 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
7. 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
10. a
f a x dx
Proof: u ax
0 du dx
x 0, u a
x a, u 0
11. a
f a x dx
Proof: u ax
0 0 du dx
f u du x 0, u a
a
x a, u 0
12. a
f a x dx
Proof: u ax
0 0 du dx
f u du x 0, u a
a
a x a, u 0
f u du
0
13. a
f a x dx
Proof: u ax
0 0 du dx
f u du x 0, u a
a
a x a, u 0
f u du
0
a
f x dx
0
14. a
f a x dx
Proof: u ax
0 0 du dx
f u du x 0, u a
a
a x a, u 0
f u du
0
a
f x dx
0
odd odd even
odd even odd
even even even