Question

The point of this question is to make sure you fully understand the logic behind volumes by slicing (and aren't just plugging it into a formula that doesn't really make any sense to you.) The way to fully understand them is to understand the picture of a slice. The base of a solid is the region in the xy-plane between the the lines y = 0, y = √√x, x= 1 and 2 = 3125. = Cross-sections of the solid perpendicular to the x-axis (and to the xy-plane) are semicircles whose diameter is on the base. (So be careful with the radius of your slices.) To get full credit for this question, please do the following: 1. Draw a picture of the full base, labeling all relevant points. (This might include needing to do some algebra to determine those relevant points. Please NEATLY show that algebra work.) 2. In that base that you drew in part 1, draw a rectangle that would represent the base of one general slice and label its width and length with appropriate variable(s). 3. Draw the picture of the slice determined by that rectangle you drew in part 2. Then indicate clearly what the volume of that slice would be (In other words, what would AV be for that slice?) Note: this volume would include variable(s). 4. Lastly, write down the integral that represents the volume of the full solid and evaluate it with technology.