Pt hoành độ giao điểm:
\(1+sinx=1\Rightarrow\left[{}\begin{matrix}x=0\\x=\pi\end{matrix}\right.\) ; \(\left[{}\begin{matrix}x=0\Rightarrow y=1\\x=\frac{\pi}{2}\Rightarrow y=2\end{matrix}\right.\)
\(sinx=y-1\Rightarrow\left[{}\begin{matrix}x=\pi-arcsin\left(y-1\right)\\x=arcsin\left(y-1\right)\end{matrix}\right.\)
\(V=\pi\int\limits^2_1\left(\pi-arcsin\left(y-1\right)\right)^2dy-\pi\int\limits^2_1arcsin^2\left(y-1\right)dy\)
\(=\pi\int\limits^1_0\left(\pi^2-2\pi.arcsint+arcsin^2t\right)dt-\pi\int\limits^1_0arcsin^2t.dt\) (với \(t=y-1\))
\(=\pi\int\limits^1_0\pi^2dt-2\pi^2\int\limits^1_0arcsintdt\)
\(=\pi^3-2\pi^2\left(t.arcsint+\sqrt{1-t^2}\right)|^1_0\)
\(=\pi^3-2\pi^2\left(\frac{\pi}{2}-1\right)=2\pi^2\)
