Question

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

y = 6 sin(x) + sin(6x)

the graph goes from x=0 to x=pi ...?

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 + (1)/(6) \int\limits^(6\pi)_0 sin(t) } \ dt \\ -6cos(x)|_0^\pi- (1)/(6)cos(t)|_0^(6\pi) \\-6(\cos\pi-\cos0)-(1)/(6)(cos(6\pi)-\cos0) \\ -6(-1-1)-(1)/(6)(1-1) \\-6(-2)-(1)/(6)*0 \\12`