exercise:6d28ed3164

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Sketch the region [math]R[/math] in the plane which is bounded by the parabola [math](y-1)^2 = x[/math], the line [math]y=2[/math], and the [math]x[/math]-axis and [math]y[/math]-axis. Find the volume of the solid of revolution obtained by rotating [math]R[/math] about the [math]x[/math]-axis, using

• formula twice, i.e., [math]\pi \int_a^b y^2dx[/math] once with [math]y-1=\sqrt{x}[/math] and again with [math]y-1=-\sqrt{x}[/math].
• the counterpart of formula, i.e., the method of cylindrical shells, for functions of [math]y[/math].