1. Find the area of the plane region bounded by the curve y = :33 and the tangent line to this curve at the point (1, 1) . 2. The base of a solid is the region between the :r-axis and the parabola y = 4 3:2. The vertical cross sections of the solid perpendicular to the yaxis are semicircles. Compute the volume of the solid. ,2 2 3. (a) Show that the area of the ellipse 32 + Eli2 = 1 is not); a ' ' . 5:32 ys 22 (b) Fmd the volume enclosed by the elllpSOld 2 + + a b2 (:2 = 1 by mtegratmg the area of a horizontal cross section. 4. Set up1 but do not evaluate an integral for the volume of the solid obtained by rotating the region bounded by the parabolas :t' = 8y 233:2 , :r = 4y yg. (a) about the :r-axis; (b) about 1; = 5; (c) about the y-axis; (d) about a: = 3. 5. Find a reduction formula for I = j (31:2 + 1)"'1 (33