Area between curves; Both dx and dy Integration. We practice setting up the definite integrals required to find the area of the region bounded by two functions. We set up definite integrals with respect to both x and y. The functions are given to us as functions of x, y=x^2 and y = 2-x. In the first segment of the video, we rewrite the equations of the curves as functions of y which will allow us to integrate with respect to y. In the second segment of the video, we set up the dx definite integral that would give the area of the region, subtracting the top function minus the bottom. In the third segment of the video, we set up the dy definite integrals that would give the area of the region, subtracting the right function minus the left. In each case, we discuss the orientation of the representative rectangle. We do not evaluate the integrals.
Tags: Area between curves; Both dx and dy Integration, Area between curves, area between two curves, area between 2 curves, area between two functions, area of a bounded region, dx, dy, definite integral