Evaluate 

Evaluate ∫sin² 3t cos 3tdt.

Find the length of the curve defined by the parametric equation x = In t and y = 1/t² between t = 1 and t = 3.

Evaluate the integral of √3t - 1  dt.

Given the area in the first quadrant bounded by x² = 8y, the line y - 2 = 0 and the y-axis. What is the volume generated when the area is revolved about the line y - 2 = 0?

Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by and about the

Determine the solution of 2x(y+1)dx − ydy = 0 where x = 0 and y = -2.

Find the general solution of (3x + 2y + 7) dx + (2x - y)dy = 0.

Solve the differential equation ydx + (3x - xy + 2)dy = 0.

Solve for the general solution of the differential equation : (D + 100) y = 0