MHB 15.2.78 But it asks for a double integral

[karush]

Use double integral to compute the area of the region
bounded by $y=4+4\sin{x}$ and $y=4-4\sin{x}$
on the interval $\left[0,\pi\right]$

View attachment 7253

ok it looks easier to do this in one $\int$ but it asks for a double $\int\int$ so ?

 

[Opalg]

Re: 15.2.78 but it asks for a double integral

Use double integral to compute the area of the region
bounded by $y=4+4\sin{x}$ and $y=4-4\sin{x}$
on the interval $\left[0,\pi\right]$
ok it looks easier to do this in one $\int$ but it asks for a double $\int\int$ so ?

$$\int_0^\pi\int_{4-4\sin x}^{4+4\sin x}dy\,dx$$ Okay, it's just a single integral in disguise, but formally it's a double integral.