Find the area of the region in two ways. a. Using integration with respect to x. 10- b. Using geometry. 00 6- 4- 2- y = 2 -x (1,1) 1 x a. Using integration with respect to x, what would be the appropriate integral to find the area? O A. ((2 -x) - ( x ) ) dx 2 O B. ( ( 2 - x ) - ( x ) ) dx O c. 2 ( x ) dx OD. 2 ( 2 - x ) dxIn the figure, the equation of the solid parabola is y = x2 18 and the equation of the dashed line is y =17X. Determine the area of the shaded region. The area of the shaded region is . (Type an exact answer.) Determine the area of the shaded region bounded by y = - x2 + 8x and y = x2 -4x. ,0 Vi The area of the region is . (Type an exact answer.) Find the area of the shaded region shown in the graph. The area of the shaded region is . (Type an exact answer.) sec 2X 2 In the figure to the right, the equation of the solid curve is y = and the equation of the dashed curve is (7 y = 2 cos 2x. Determine the area of the shaded region. The area of the shaded region is . (Type an exact answer.) Find the area of the region enclosed by the curves y=3cosxand y=3cost fOI'OSXSTE. W y=3cos 2x Set up the integral(s) that will give the area of the region. Select the correct choice below and fill in any answer box(es) to complete your choice. Express the area of the following shaded region in terms of (a) one or more integrals with respect to x, and (b) one or more integrals with respect to y. y = 8x - 128 (a) What is the area of the region in terms of x? 16 O A. (x2 - 24X - 128) dx 0 16 OB. (-x2 + 24X + 128) dx 0 8 16 Oc. (-x2+ 16x) dx + (-8x + 128 ) dx 0 8 8 16 OD. J (x2 - 16*) ax + (8x-128)dx o 8Find the area of the region described. The region bounded by y = 2(x + 1), y = 3(x + 1), and x = 2 The area of the region is ( Type an exact answer. )Find the area of the region described. 2 Q} The region bounded by y= 2 and y=1 1 +x The area of the region is D. (Type an exact answer.) Find the area of the region described. The region bounded by y = 12,288J; and y = 192x2 \\0 The area of the region is D. (Type an exact answer.) 4 Find the area of the region in the first quadrant bounded by the line y = 4x, the line x = 5, the curve y = g, and the x-axis. The total area of the region is El. (Type an exact answer, using radicals as needed.) Find the area of the region described. X The region bounded by y = |x - 16| and y = X The area of the region bounded by y = |x - 16| and y = 3 is (Type an exact answer, using radicals as needed.)Find the area of the region described. \\33 TE The region in the first quadrant bounded by y = 2 and y = 2 sin X on the interval [05] The area of the region is E. (Type an exact answer, using it as needed.) Find the area of the region described. \\\\: