Question

Find the area of the region. Use a graphing utility to verify your result.

Answer 1

$\int\limits^\pi_0 [6 \sin{x} + \sin(6x) }] \, dx \\ \int\limits^\pi_0 {6 \sin{x}}\ dx + \int\limits^\pi_0 \sin(6x) } \ dx \\ 6\int\limits^\pi_0 { \sin{x}}\ dx + \frac{1}{6} \int\limits^{6\pi}_0 \sin{t} } \ dt \\ -6\cos{x}|_0^\pi- \frac{1}{6}\cos{t}|_0^{6\pi} \\-6(\cos\pi-\cos0)-\frac{1}{6}(\cos{6\pi}-\cos0) \\ -6(-1-1)-\frac{1}{6}(1-1) \\-6(-2)-\frac{1}{6}\times0 \\12$