Question

$\int_{0}^{20\pi} (|\sin x| + |\cos x|)^2 \,dx$
is equal to

• A. $10(π+4)$
• B. $10(π+2)$
• C. $20(π-2)$
• D. $20(π+2)$

Answer 1

Answer: (D)

$20(π+2)$

Answer 2

The correct answer is (D) : 20(π+2)
$\int_{0}^{20\pi} (|\sin x| + |\cos x|)^2 \,dx$
$20 \int_{0}^{\pi} (1 + |\sin(2x)|) \,dx$
$40 \int_{0}^{\frac{\pi}{2}} (1 + \sin(2x)) \,dx$
$40 \left( x - \frac{\cos(2x)}{2} \right) \Bigg|_{0}^{\frac{\pi}{2}}$
$= 40(\frac{\pi}{2}+\frac{1}{2}+\frac{1}{2})$
$= 20(\pi +2)$