B Consider the shaded region bounded by y=x2 – 4 and y= 3x + 6 (see above). Note that the r-axis and y-axis are not drawn to the same scale. (a) Find the coordinates of the points A, B, and C. Remember to show all work. (b) Set up but do not evaluate an integral (or integrals) in terms of r that represent(s) the area of the region. That is, your final answer should be a definite integral (or integrals)....
Find the area of the region bounded by the graphs of the given equations. y=x, y=24/7 Set up the integrals) that will give the area of the region. Select the correct choice below and fill in any answer box(es) to complete the choice ОА dx OB The area is (Type an integer or a simplified fraction)
1. Consider the region bounded by the y-axis and the functions y and y-8 Set up (but do not evaluate) integrals to find (a) The area of this region. (b) The volume of the solid generated by rotating this region about the y ad sn axis using shells. (c) The volume of the solid generated by rotating this region about the vertical line r5 using washers 2. Set up (but do not evaluate) an integral to ind the work done...
Find the area of the region bounded by the graph of the equation. 5. Y = va, X = 1, x = 8, y = 0 y = 0 x = 4, x = 1, 6. y = x2 + 3,
2 (1o pts) Gven the region bounded hy the graphs x -yo, and y 2 a Sketch a graph of the region. b. Set up the nvo iterated integrals (based upon the rwo choices for order of integration) that represent the area of the region. c Solve either of the two integrals in part b) to find the area of the region -54 3 2-1 2 (1o pts) Gven the region bounded hy the graphs x -yo, and y 2...
A region Q is bounded by y=x^3 , x=3 and y=-8. Find the area of region Q.
Find the volume of the given solid region bounded below by the cone z = \x² + y2 and bounded above by the sphere x2 + y2 + z2 = 8, using triple integrals. (0,0,18) 5) 1 x? +y? +22=8 2-\x?+y? The volume of the solid is (Type an exact answer, using a as needed.)
1. Find the mass and centroid of the region bounded by the = y2 with p (a, y) parabolas y x2 and x 2. Set up the iterated (double) integral(s) needed to calculate the surface area of the portion of z 4 2 that is above the region {(«, у) | 2, x < y4} R 2 Perform the first integration in order to reduce the double integral into a single integral. Use a calculator to numerically evaluate the single...
3. (10 pts) Find the area of the region bounded between y = xe-*?, , y = x + 1, x = 2 and the y-axis. Note that the graph of the region is provided below. You can leave your answer in terms of e. y=x+1 x2 X-0 0 0.5 1. 0 dy Use the Fundamental Theorem of Calculus to find dx for y = = L* sin (t2)dt.
Find the area of the region described. The region in the first quadrant bounded by y = 1 and y=sin x on the interval The area of the region is (Type an exact answer, using a as needed.)