The region bounded below by the parabola y = x2 and above by the line y = 4 is to be partitioned into two subsections of equal area by cutting across it with the horizontal line y = c. a. Sketch the region and draw a line y = c across it that looks about right. In terms of c, what are the coordinates of the points where the line and parabola intersect? Add them to your figure. b. Find c by integrating with respect to y. (This puts c in the limits of integration.) c. Find c by integrating with respect to x. (This puts c into the integrand as well.)
The region bounded below by the parabola y = x2 and above by the line y = 4 is to be partitioned into two subsections of equal area by cutting across it with the horizontal line y = c. a. Sketch the region and draw a line y = c across it that looks about right. In terms of c, what are the coordinates of the points where the line and parabola intersect? Add them to your figure. b. Find c by integrating with respect to y. (This puts c in the limits of integration.) c. Find c by integrating with respect to x. (This puts c into the integrand as well.)
The region bounded below by the parabola y = x2 and above by the line y = 4 is to be partitioned into two subsections of equal area by cutting across it with the horizontal line y = c. a. Sketch the region and draw a line y = c across it that looks about right. In terms of c, what are the coordinates of the points where the line and parabola intersect? Add them to your figure. b. Find c by integrating with respect to y. (This puts c in the limits of integration.) c. Find c by integrating with respect to x. (This puts c into the integrand as well.)
The region bounded below by the parabola y = x2 and above by the line y = 4 is to be partitioned into two subsections of equal area by cutting across it with the horizontal line y = c. a. Sketch the region and draw a line y = c across it that looks about right. In terms of c, what are the coordinates of the points where the line and parabola intersect? Add them to your figure. b. Find c by integrating with respect to y. (This puts c in the limits of integration.) c. Find c by integrating with respect to x. (This puts c into the integrand as well.)
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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