Consider the following integral. Sketch its region of integration in the xy-plane. CC T dx dy (a) Which graph shows the region of integration in the xy-plane? C (b) Write the integral with the order of integration reversed: | with limits of integration B D I dx dy In(x) C I In(x) dy dx A = B= C = D= (c) Evaluate the integral. e 2 9 (Click on a graph to enlarge it) D B 02

c) Consider the following two functions are given: y = 2x − x² and y = x². Sketch the two curves on the same pair of axes for the interval 0 ≤ x ≤ 1 and show the following on the graph: y-intercepts, x- intercepts, and points of intersection. Shade the area bounded between the two curves. i. ii. Use integration to find the shaded area in Part (i) (area enclosed between the curves).

Let f(z) = -a? + 6z – 5. Estimate the area below the curve y = f(x) and above the x-axis using 100 rectangles and a right hand rule. -를 +3r2-Sx + o, ▲ Submit answer

Q1.A: Find the area of the shaded region shown in figure (1). dud y = 1 y = x2 x 1+ y2 Figure (1) y = -1