MAT 266 Lecture 16: Volume by Slicing and Shells
Document Summary
Mat266 lecture #16 7. 2 volume by slicing/7. 3 shells. Example: the region given is bounded by y = x^2 and y = sqrt(x). Find the volume of the solid obtained by rotating r around the points: x =2, y =3, y = -1, x = -2. Find zeroes for both x, y: x=2, rotate around the vertical line. When finding the radius, we get it in terms of x but because we are slicing horizontally we need to plug it back into the original functions to get it in terms of y. Once you find the inner and outer radius, plug into the volume formula: y = 3. Since we are going to slice vertically, when finding the radius it needs to be in terms of x. Inner radius: 3-y --> 3 - sqrt(x: y = - 1 graph, then use the washer method. Slice vertically do we are going to put function in terms of x.
