For $a, b \gt 0$ let $F(a, b)=\int_a^b|\sin 2 \pi x| d x$. Then

• Correct answer
  A

  $F(10,11)=2 F\left(0, \frac{1}{2}\right)$
• B

  $F\left(\frac{41}{4}, \frac{43}{4}\right)=\frac{1}{2} F\left(\frac{1}{2}, 1\right)$
• C

  $F\left(\frac{1}{8}, \frac{1}{4}\right)=F(1,2)$
• Correct answer
  D

  $F\left(\frac{41}{4}, \frac{43}{4}\right)=\frac{2}{3} F\left(0, \frac{3}{4}\right)$

Hence, the correct answer is options: 'A', 'D'.