Consider the following equations. x) - x5+5 g(x) - x+5 Sketch the region bounded by the graphs of the equations. 3 3 2 2 1 -3 -2 -1 -2 -1 -3 -2 -1 -1 Find the area of the region.

The figure on the right shows a quadratic curve and a straight line with respective equations y = 4 X x² and y = 2. Let A and B be the points at which the curve and the line intersect. A y=4-x-x² B y = 2 X Calculate the area of the finite region bounded by the quadratic curve and the straight line, shown shaded in the above figure. Area =

Use right and left endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. f(x) = 2x + 2, [0, 2], 4 rectangles Step 1 To find two approximations of the area of the region between the graph of the function f(x) = 2x + 2 and the x-axis over the interval [0, 2] using 4 rectangles, first partition the interval [0, 2 ] into n = Then the width of each rectangle is given by using the following formula. b - a Step 3 Ax = Step 2 Therefore, the width of each rectangle is b - a n Ax = n -0.5 4 Consider the right endpoints approximation of the area of the region. Then substitute Ax = 2 Observe the region between the graph of the function f(x) = 2x + 2 and the x-axis over the interval [0, 2] with four circumscribed rectangles, which is shown below. Submit - 0 6 5 3 0.5 1.0 The right endpoints of the n intervals are Ax(i) where i = 1 to 4 1.5 Thus, the right end points of four…

Consider the following equations. y = -x² + 2x + 2 y = -x + 2 Sketch the region bounded by the graphs of the equations. y -10 -10 -5 -5 10 5 -5 -10F y 10 5 -5 - 10 Find the area of the region. 5 5 10 10 y 10 10 5 5 X X -10 -5 5 10 - 10 -5 5 -5 -5F -10 X -10F 10 X

7. The figure shows a rectangle drawn inside the region, in the first quadrant, enclosed by the r-axis, the y-axis and the graph of y = 7– 2x. The right vertical side of the rectangle passes through the point (r, 0) as shown in the figure. Rectangle (a) Explain why the area A(a) of the rectangle must be A(r) = 7x-2.r? 1) (b) What is the largest possible area of such a rectangle? Write down the steps leading to your answer.

Consider the following equations. y = x²-9 y = -x + 5 X = 0 X = 2 Sketch and shade the region bounded by the graphs of the functions. (Use solid lines for the boundaries.) No Solution Help -6 -5 -4 -3 Find the area of the region. -2 -1 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 2 3 4 5 6 Clear All Delete Fill WebAssign. Graphing Tool Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties.