Please answer as many questions as possible if not all

1. Evaluate each of the following integrals. (i) J(Bx 6x* +4x3)7(1 4x +4x*) dx (ii) I(x+1)(x2+16) dx (iy [ sin5(x) cos?(x) dx (iv) [ tan(x) sec (x) dx v) Jx*+x+1D)In(x3)dx 2. Find the centroid of the region bounded above by the semi-circle y = V4 x? and below by x-axis 3. Sketch the region bounded by the curves y = 2x? and y = 6 4x? and find the area of the region. 4. Find the volume of the solid generated by rotating the region bounded by the curves in Question 3, in the first quadrant around the y-axis, using the shell method. 5. Consider the curve given parametrically by x(t) = ef, y(t) = e*, Answer each of the following: (i). Give an integral for the area of the surface generated by rotating the curve around x-axis for t [0,4] . (ii) Show that this equation represents the curvey = x%,x > 0,y >0 6. Find the length of the curve y = In(secx),0