Question

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = 5x⁴,   y = 5x,   x ≥ 0;    about the x-axis

Find the area of the region enclosed by the given curves.

y = 3 cos(πx),    y = 12x² − 3

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

2x = y²,  x = 0,  y = 5;  about the y-axis

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.

y = x³,    y = 0,    x = 1,    x = 2

Answer 1