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Magazine Problem 127
Use shells to find the volumes of the given solids. Note that the rotated regions lie between the curve and the \(x\) -axis and are rotated around the \(y\) -axis. \(y=\sqrt{x}, x=0,\) and \(x=1\)
Problem 128
Use shells to find the volumes of the given solids. Note that the rotated regions lie between the curve and the \(x\) -axis and are rotated around the \(y\) -axis. \(y=\left(1+x^{2}\right)^{3}, x=0,\) and \(x=1\)
Problem 129
Use shells to find the volumes of the given solids. Note that the rotated regions lie between the curve and the \(x\) -axis and are rotated around the \(y\) -axis. \(y=5 x^{3}-2 x^{4}, x=0,\) and \(x=2\)
Problem 130
Use shells to find the volume generated by rotating the regions between the given curve and \(y=0\) around the \(x\) -axis. \(y=\sqrt{1-x^{2}}, x=0,\) and \(x=1\)
Problem 132
Use shells to find the volume generated by rotating the regions between the given curve and \(y=0\) around the \(x\) -axis. \(y=e^{x}, x=0,\) and \(x=1\)
Problem 133
Use shells to find the volume generated by rotating the regions between the given curve and \(y=0\) around the \(x\) -axis. \(y=\ln (x), x=1,\) and \(x=e\)
Problem 134
Use shells to find the volume generated by rotating the regions between the given curve and \(y=0\) around the \(x\) -axis. \(x=\frac{1}{1+y^{2}}, y=1,\) and \(y=4\)
Problem 136
Use shells to find the volume generated by rotating the regions between the given curve and \(y=0\) around the \(x\) -axis. \(x=\cos y, y=0,\) and \(y=\pi\)
Problem 140
Find the volume generated when the region between the curves is rotated around the given axis. \(y=3-x, y=0, x=0,\) and \(x=2\) rotated around the \(y\) -axis.
Problem 141
Find the volume generated when the region between the curves is rotated around the given axis. \(y=x^{3}, y=0,\) and \(y=8\) rotated around the \(y\) -axis.
