Finding the Area of a Region In Exercises 31-36, (a) use a graphing utility to graph the region bounded by the graphs of the functions, (b) find the area of the region analytically, and (c) use the
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EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- Using the Fundamental Theorem of Calculus find the area of the region bounded by the x-axis and the graph of f(x)=−x2−1x+12.arrow_forwardA right triangle has one vertex on the graph of y =x°, x> 0, at (x, y), another at the origin, and the third on the positive y-axis at (0, y), as shown in the figure. Express the area A of the triangle as a function of x. y = x (0, у) (x, y) A(x) = %3D (Use integers or fractions for any numbers in the expression.) -> (0, 0)arrow_forwardA right triangle has one vertex on the graph of y = x, x>0, at (x, y), another at the origin, and the third on the positive y-axis at (0, y), as shown in the figure. Express the area A of the triangle as a function of x. y=x5 (0. y) (x, y) A(x) =D (Use integers or fractions for any numbers in the expression.) (0, 0)arrow_forward
- Sketch the graphs of the functions f and g. f(x) = square root of x , g(x) = − 1/2x -4 Then, Find the area of the region enclosed by these graphs and the vertical lines x = 4 and x = 9.arrow_forwardEXAMPLE 6 Find the area of the region enclosed by the curves y = 1/x, y = x, and y = x, using (a) x as the variable of integration and (b) y as the variable of integration. SOLUTION The region is graphed in Figure 14.arrow_forwardSurface Area The roof over the stage of an open air theater at a theme park is modeled by f(x, y) = 25[1 + e−(x2+y2)1000 cos2(x2 + y2/ 1000 )] where the stage is a semicircle bounded by the graphs of y = √502 − x2 and y = 0. Use a computer algebra system to approximate the number of square feet of roofing required to cover the surface.arrow_forward
- find the area of a region if the graphs are f(x)=(x-5)1/3 g(x)=x-5arrow_forwardQuestion Determine the area, in square units, of the region bounded by f(x) = 10x³ + x² - 21x-9 and g(x) = 9x³ + x² − 5x - 9 over the interval [2, 6]. Provide your answer below: Content attribution FEEDBACK MORE INSTarrow_forwardf(x) = x2 − 4x + 5 (a) Express f in standard form. f(x) = (b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist, enter DNE.) vertex (x, y) = x-intercept (x, y) = y-intercept (x, y) = (c) Sketch a graph of f. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. (d) Find the domain and range of f. (Enter your answers using interval notation.) domain rangearrow_forward
- A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 - x, as shown in the figure. Each piece is bent into the shape of a square. 10 cm (a) Find a function that models the total area enclosed by the two squares. A(x) = (b) Find the value of x that minimizes the total area of the two squares X = cmarrow_forwardQuestion If R is the region between the graphs of the functionsf(x) = 8x³ + 7x² + 28x + 6 and g(x) = 7x³ – 6x² – 8x + 6 over the interval [-2, 2], find the area, in square units, of region R.arrow_forwarda) Find the function's domain (b) Find the function's range (c) Describe the function's level curves (d) Find the boundary of the function's domain (e) Determine if the domain is an open region, a closed region , or neither (f) Decide if the domain is bounded or unbounded for: f(x,y) = ln(x^2 + y^2)arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage