Sect 15.3 Enhanced Assignment

Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Student: Jalen Wilson Date: 07/11/24 Assignment: Sect 15.3 Enhanced Assign 1. Sketch the region bounded by the given line and curve. Then express the​region's area as an iterated double integral and evaluate the integral. 2 The parabola x = − y and the line y = x + 20 Sketch the region. Choose the correct graph below. A. B. 30 C. y 30 x -30 y D. 30 y x 30 -30 -30 30 y x 30 -30 -30 30 x -30 -30 30 -30 Express the shaded area as an iterated integral. Select the correct choice below and fill in the answer boxes to complete your choice. − 16 A. A = ∫ ∫ 0 4 B. A = dx dy + ∫ 2 −y ∫ ∫ −5 y − 20 The value of the integral is ∫ 243 2 dx dy . ​(Simplify your answer. Type an integer or a​fraction.) dx dy 2. Sketch the region bounded by the given lines. Then express the​region's area as an iterated double integral and evaluate the integral. x y = ​x, y = 2 ​, and y = 2 Sketch the region. Choose the correct answer below. A. B. 4 y C. y 4 2 4 2 -4 -4 -4 4 -2 y 4 2 x 4 -2 y 2 x -8 D. x 8 -8 -4 -2 -4 x 4 -4 -4 4 -2 8 -4 Express the shaded area as an iterated integral. Select the correct choice below and fill in the answer boxes to complete your choice. 2 A. A = ∫ ∫ 0 B. A = ∫ dx dy + 2 2y ∫ ∫ 0 y The value of the integral is ∫ dx dy dx dy 2 . ​(Simplify your answer. Type an integer or a​decimal.) 3. The sum of integrals below give the area of a region in the​xy-plane. Sketch the​region, label each bounding curve with its​equation, and give the coordinates of the points where the curves intersect. Then find the area of the region. 0 8−x ∫ ∫ 9 dydx + 8−x ∫ ∫ dydx 0 − x/9 − 1 − 9x Sketch the​region, label each bounding curve with its​equation, and give the coordinates of the points where the curves intersect. Choose the correct answer below. A. B. 6 y y= − 12 x 9 -6 y 12 (1,9) (9,1) y ( − 1,9) x y=8−x 12 y = − 9x C. y=8−x y = − 9x x y=8−x -12( − 9, − 1) y= − ( − 1, − 9) -12 x 9 -6 6 y = − 9x x -6 y= − -6 The area of the region is 40 . ​(Type an integer or a simplified​fraction.) 2 2 4. Find the average height of the paraboloid z = x + y over the square 0 ≤ x ≤ 2​, 0 ≤ y ≤ 2. The average height is 8 3 . ​(Type an integer or a simplified​fraction.) x 9 (9, − 1) 12