Problem Calculate the area of the shaded region between the curves and the x-axis in the...
1. Determine the area of the region between the two curves y=x' and y = x + 2x by integrating over the x-axis. Hint: Refer the figure and note that you will have two integrals to solve by splitting the region between the two curves into two smaller regions. W t.
Find the area of the region between curves 1. Find Find the area of the region between curves by rotating about x-axis the region in the x,y- plane bounded below and above, respectively, by the curves: a. y = 2x2, y = 4x + 16 b. x = -y2 + 10, x = (y – 2) I
16 pts) 1. Determine the area of the region between the two curves y=x and y+2x by integrating over the x-axis. Hint: Refer the figure and note that you will have two integrals to solve by splitting the region between the two curves into two smaller regions. lo pl [6 pts) 2. Find the area of the region bounded by the curves y=12 - x, y=vx, and y20
Find the total area of the shaded region. The total area of the shaded region is 1 (Type an exact answer, using * as needed.) Ay y2 y-200x²x R/2 3/2 2x
Find the area of the shaded region bounded by y = 2x and y = xV49 – x2 in the figure. 2. (Give an exact answer. Use symbolic notation and fractions where needed.)
Problem 3. (25 points total) Determine (a) The area A of the shaded region. (b) The x location of the centroid of the shaded area, which is called x. (Use an integral to confirm the value found by inspection from symmetry.) (C) The y location of the centroid of the shaded area, which is called y. (d) The moment of inertia, Ix, of the shaded area about the x axis. (e) The moment of inertia, ly, of the shaded area...
(b) the volume of the solid generated by revolving the region about the x-axis. (c) the volume of the solid generated by revolving the region about the line x-3 The shaded region below is bounded by the curves y e 2x,y e* and the line x 1. A- 3 y ex 2 yežx Find the area of the shaded region. ) Using washer method, find the volume of the solid generated by revolving the region about the line y -2.
d) Find the area between the two curves (the shaded region). 2 + (2 r=2+cos 2θ ra sin 2θ d) Find the area between the two curves (the shaded region). 2 + (2 r=2+cos 2θ ra sin 2θ
1. The area of the shaded region in the figure could be found by one or more integrals with respect to either .x or y. Use the graph to help answer the following: .. Does the integrat (w - V*)s give the area of the region? Explain why or why not. (3 pts.) YA lyx y=Vx b. Set up and evaluate a definite integral with respect to x to find the exact area of the shaded region (5 pts.)
Find the total area of the shaded region The total area of the shaded region is (Simplify your answer.) AY 18 @ 14 12 10 y-9 Y 36 Find the area of the triangle with (1, -1, -2), (-2,0, -1), and (0, -2,1) as vertices. The area of the triangle is square units. (Type an exact answer, using radicals as needed.)