4. 5. (a) Sketch the region bounded by y- +2x-4, y-x2+4x-4 clearly indicating vertices on the gra...
The region R is bounded by the x-axis and y = V16 – x2 a) Sketch the bounded region R. Label your graph. b) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) da c) R
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)....
5) Given the function fix.y) - x2 and region R bounded by x 0, y x and 2x+y 6 (a) Sketch the region R (label lines, intercepts, axes and shade region) (b) SET UP the integral over this region (c) Assuming f(x.y)- xa is the density function for the lamina R given above, determine the mass for R 5) Given the function fix.y) - x2 and region R bounded by x 0, y x and 2x+y 6 (a) Sketch the...
[4] Sketch the region bounded above the curve of y = x2 - 6, below y = x, and above y = -x. Then express the region's area as on iterated double integral ans evaluate the integral. -4 -3 -2 -1 0 1 2 3 4 [5] Find the area of the region bounded by the given curves x - 2y + 7 = 0 and y2 -6y - x = 0.
practice 1. Find the area of the region bounded by the curves. y= x2 - 4x, y = 2x
2) The region R is bounded by the x-axis and y = V16 - x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Ry region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) dA R
2) The region R is bounded by the x-axis and y = V16 - x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) dA R
2) The region R is bounded by the x-axis and y = V16 – x2. a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. S sec(x2 + y2) tan(x2 + y2) da R
2) The region R is bounded by the x-axis and y = V16 – x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. S sec(x2 + y2) tan(x2 + y2) da R
3. Let region R be bounded by y = 2x - x? and y = 0 on (0,2). Setup the definite integral(s) that represents the volume of the solid generated by rotating region about the y-axis. Draw a sketch to interpret your results.