Question 1 1 pts Evaluate the integral. 9- x2 x dy dx O 27 O 81 4 O 27 0 9 Question 2 1 pts Integrate the function f over the given region. f(x, y) = y2 ex over the triangular region in the first quadrant bounded by the lines x = y/6, x = 1, y = 0 18(e - 1) 0 72(e - 1) O 216(e + 1) 18eQuestion 3 Write an equivalent double integral with the order of integration reversed. 6 Inx 9x dy dx O In 6 6 9x dx dy e V O In 6 6 9x dx dy O In 6 6 54x dx dy eV O In 6 6 54x dx dyQuestion 4 Reverse the order of integration and then evaluate the integral. g I COSX (1X d" X . 9'4 Q 4sin2 Q 25in4 Q 2cos4 Q 4c052 Question 5 Find the volume of the indicated region. the region bounded by the paraboloid z=x2 + _v2 and the plane 2 = 100 0 250011 Question 6 1 pts Evaluate the double integral over the given region. 3x sin xydA, R: O S X S n, Osys 1 On O 37t - 3 O 3nt Question 7 1 pts Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries. z = x2 + y2; O s xs 1, 0 sys1 O w / co O W/ A O O WINQuestion 8 1 pts Express the area of the region bounded by the given lineis) and/or curve(s) as an iterated double integral. The coordinate axes and the line x + _v = 7 O i I'M T 7): Oi i Question 9 Find the average value of the function f over the given region. f(x, y) = ex over the region bounded by y = 2x, y= 10x , x =0, and x= 1 . O Ze - 1 4 Oe-1 2 Oe - 1 O 2e - 1Question 10 Change the Cartesian integral to an equivalent polar integral, and then evaluate. 81 - x2 dv dx -9 O 729n 2 817 2 O 9TL 2 OQuestion 11 Find the area of the region specified in polar coordinates. the region enclosed by the curve r = 7 cos 30 O 49 4 O 49 O 49 2 O 49 6Question 12 1 pts Solve the problem. Find the average distance from a point P(x, y) in the first two quadrants of the disk x2 + s81 to the origin. 0 6 O 0 3 OQuestion 13 Solve the problem. Rewrite the integral 8 10(1 - z/8) 6(1 - v/10- z/8) dx dy dz in the order dz dy dx. C 6 10(1 - x/6) 8(1 - x/6 - v/10) dz dy dx O 8 10(1 - z/8) 6(1 - v/10- z/8) dz dy dx O 8 10(1 - x/6) 6(1 - x/6 - v/10) dz dy dx O 6 10(1 - z/8) 8(1 - v/10- z/8) dz dy dx