(a)
(b)
The iterative integral would be when we integrate with respect to 'x' to get the area bounded by the curves.
When we are to integrate with respect to 'x' then we need to have function in terms of 'x' that is f(x) or g(x)
Here a = 1 and b = 5
=>
The other iterative integral would be when we integrate with respect to 'y' to get the area bounded by the curves.
When we are to integrate with respect to 'y' then we need to have function in terms of 'y' that is f(y) or g(y)
Here a = 0 and b = 2
(c)
Lets solve the second iterative integral that we found in part (b) in order to find the area bounded by the curves.
As this is a bit easier to solve in comparison to the other one.
=
=
= units square --------> This is the area bounded by the curves
2 (1o pts) Gven the region bounded hy the graphs x -yo, and y 2 a Sketch a graph of the region. b...
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
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
Sketch the region bounded by the graphs of y = x2 and y = 2-x then find its area. od
Problem 2. Sketch the region R in the first quadrant bounded by the lines y = 3x and the parabola y = 12. Compute the area of R using (a) vertical and (b) horizontal slices. Then set up integrals for the volume of the solid obtained by rotating the region R about the x-axis. Use (c) vertical and (d) horizontal slices. (35 pts, 10 mts]
show all work please (5 pts) Find the area of the region bounded by the graphs of y + 2 and y = [ +1,0 < x < 2. 2 Sketch the region.
2. Sketch the region bounded by the graphs of the equations and find the area of the region f(x) = x2 + 2x +1 g(x) = 3x +3
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)