(A) Sketch the region in the x, y plane corresponding to the double integral 2x ** 2y sin(x) dy dx. (B) Calculate the integral in the order where y is integrated first and a second. (C) Calculate the integral in the order where x is integrated first and y second.

Sketch the graph the integrands and use areas to evaluate the integrals. La |(1- l2) dx а. -1 3/2 (-2х + 4) dx J1/2 b.

Needed to be solved correclty in 1 hour completely and get the thumbs up please show neat and clean work.box answer should be right

Please explain how to set the integral

Consider the double integral H T-arcsin y = S S sin (cos(x)) dxdy. Sketch the region of integration of H. Calculate the double integral H, by changing the order of integration.

Consider the planar region in the first and fourth quadrants between the circles of radius 2 and 4. (a) Shade the region on the diagram below (or make your own shaded sketch) (b) Find the double integral of the function f (x, y) = x over this region.

Fast

Shade the region in quadrants I and IV which lies inside the curve r² = 8 cos (20) and outside the curve r=2. Then, set up but DO NOT EVALUATE the integral to find the shaded area.

Say that you need to compute a double integral of the function f(x,y)=xy over the region D bounded by the x-axis, y=x, x2+y2=1, and x2+y2=16. Explain in words and/or show in a picture why this would be (unnecessarily) complicated in Cartesian coordinates. Then, setup and evaluate the integral using polar coordinates.

Consider the region T bounded by the graphs of y = x2, y = -3x, and x = 4. (a) Find the area of T. (b) Find the volume of the solid formed by rotating Tabout the horizontal line y = -12. (c) Write, but do not evaluate, an expression involving one or more integrals that gives the perimeter of T. + dx