MAT1505-03/04 15F Quiz 5 Print Name (Last, First) __________________ , _______________|____Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use EQUAL SIGNS and arrows when appropriate. Always SIMPLIFY expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation when appropriate). Indicate where technology is used and what type (Maple, GC).1. The curve 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 over the interval LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJiZsZXE7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GMzYtUSI8RidGL0Y2RjlGO0Y9Rj9GQUZDRkVGSC1GSzYlUSJSRidGTkZRRi8= is rotated around the 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.a) Let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiSEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= designate the average value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= over this interval. Write down a simplified definite integral for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and then evaluate it by hand showing all your steps, and make sure it agrees with Maple's evaluation.b) Make a diagram of this curve over this interval and include a horizontal line for this average value. Does the rectangle it makes appear to have the same area as that above the curve? Explain.c) Let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= denote the volume of a solid formed by revolving this curve segment around the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-axis, and indicate a typical vertical cross-section of the integration region needed to evaluate this volume, labeling its endpoints appropriately to justify your limits of integration and indicating how you obtained your integrand. Write down a simplified definite integral for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and then use Maple to evaluate it.d) Compare this solid with a cylinder of revolution about the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-axis. What radius would the cylinder need to have for it to have the same volume?solutiona) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==QyU+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqJkkiaEdGJSIiIi1JI2xuR0YlNiMsJkYvRi8qJjkkRi9JIlJHRiUhIiJGN0YvRjdGJUYlRiVGLy1GJEYnQyw+SSJSRzYiIiIiISIiPkkiaEdGJUYmRictSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiUtSSJmR0YlNiNJInhHRiUvRjM7IiIhRiQvSSpncmlkbGluZXNHRiVJJXRydWVHRi1GJj5GKS5GKUYnPkYkLkYkRic=Qys+SSJSRzYiIiIiISIiPkkiaEdGJUYmRictSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiUtSSJmR0YlNiNJInhHRiUvRjM7IiIhRiQvSSpncmlkbGluZXNHRiVJJXRydWVHRi1GJj5GKS5GKUYnPkYkLkYkThe average:Qy8+SSJSRzYiIiIiISIiPkkiaEdGJUYmRic+SSJIR0YlKiZGJEYnLUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQtSSJmR0YlNiNJInhHRiUvRjY7IiIhRiRGJkYmPkYpLkYpRic+RiQuRiRGJ0YsRiYqJkYkRictRi42JEYzRjZGJg==Qyw+SSJSRzYiIiIiISIiPkkiaEdGJUYmRictSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiU3JC1JImZHRiU2I0kieEdGJUYmL0Y0OyIiIUYkL0kqZ3JpZGxpbmVzR0YlSSV0cnVlR0YtRiY+RikuRilGJz5GJC5GJEYnThe volume:JSFHQyU+SSJWRzYiLUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqJkkjUGlHRikiIiItSSJmR0YlNiNJInhHRiUiIiMvRjI7IiIhSSJSR0YlRi4tRic2JEYsRjI=