Answer with explanation:
The equation of two curves are
y=8 sin x
y=8 cos x
The point of intersection of two curves are
→8 sin x=8 cos x
sinx = cos x
[tex]x=\frac{\pi}{4}\\\\y=8\sin\frac{\pi}{4}\\\\y=4\sqrt{2}[/tex]
When you will look between points , 0 and [tex]x=\frac{\pi}{4}\\\\y=8\sin\frac{\pi}{4}\\\\y=4\sqrt{2}[/tex],the curve obtained is right angled triangle.
Now, rotate the curve that is right angled triangle along the line , y= -1, to obtain a shape similar or resembling with Right triangular prism.
Draw a circular disc in the right triangular prism , having radius =x,and small part on the triangle having length dx.dx varies from 0 to [tex]\frac{\pi}{4}[/tex].
Required volume of solid obtained
[tex]=\int\limits^{\frac{\pi}{4}}_0 {8 \sin x} \, dx \\\\=|-8\cos x|\left \{ {{x=\frac{\pi}{4}}} \atop {x=0}} \right.\\\\=8-4\sqrt{2}[/tex]
=8-4√2 cubic units
