Question

Let f(x) = sin5x − sin75x + sin1000x, 0 ≤ x ≤ 2π. Then R 2π
0
|f(x)|
2dx equals
1. 11
3
2. 3π
3. 16
3
4. 8
5

Answer 1

Step-by-step explanation:

solution: Correct option is C)

sin5x+sin3x+sinx=0

(sin5x+sinx)+sin3x=0

sinC+sinD=2sin

2

C+D

cos

2

C−D

2sin3x⋅cos2x+sin3x=0

sin3x(2cos2x+1)=0

sin3x=sin0 or 2cos2x+1=0

3x=nπ cos2x=cos2π

/3

x=

3

nπ

2x=2π

/3

+2nπ

0≤x≤π

/2

x=π

/3

±nπ.

x=nπ

/3

gives, x=0,π

/3

.