Integration Practice, Area Between curves

A/Evaluate these integrals 3 23¶u3du = 34 u4 32|= 195 4 10¶ u1/2du = 23 u3/2 10|= 23 14 91¶ u3/2du = 121 5 6) 81¶ (1 + x1/3)3 x2 /3 5) dx /4 04) ¶ tan x sec2x dx 20¶ x(1 + 2x2)3/2 dx 25 16 ¶ 12 u −12 du = u 12 25 16 − cos x | = 1 0( |= 2 13 x3 − 3x2 + 2x) 31|= −38 3 3) 30¶ x x2 + 16 dx 2) 01) ¶ sin x dx 13¶(x2 − 6x + 2) dx ____________________________________________ B/Draw a diagram for and solve each of the following: 1) Find the area of the region bounded by y = x 2 and y = 2 – x 2. Integration & Area Between Curvesy = x2 y = 2 -x2 A = 2 10¶ (2 − 2x2) dx = 83 . Integration & Area Between Curves2) Find the area of the region bounded by the graphs of x = 2y , y = 2x – 6, and y = 0 Integration & Area Between Curves4 x = 2y y = 2x -6 3 A = 30¶ 12 x dx + 43¶ ( 12 x − 2x + 6) dx = 3 . Integration & Area Between Curves3) Find the area of the region bounded by x = y 2 – 1 and x = y + 1. Integration & Area Between Curvesto find the points of intersection, set y + 1 = y2 – 1 to get y = – 1 or 2. -12 3 A = 2 −1 ¶ (y + 2 − y2) dy = 92 Integration & Area Between Curves