By: Meghan Grubb Shells Method

Shells With this method, you draw a line segment parallel to the axis of rotation Forms a cylinder Surface Area = 2∏rh Volume = X is radius [f(x)-g(x)] is height

Example First step – graph the lines given Second step – find points of intersection Third step – about y-axis, draw line parallel to y – axis If about x-axis, draw line parallel to x-axis Fourth step – put 2∏ in front of integral Fifth step – plug in boundary limits dx – use x intercepts, dy – use y intercepts Sixth step – multiply Radius and Height Seventh step – plug dx or dy

Radius

Height Dx problem – top line minus bottom line Dy problem – right line minus left line

Example

Example

Example First step – graph the lines given Second step – find points of intersection Third step – dx? Or dy? Draw line parallel to y = -3 Dy because line is parallel to y-axis Fourth step – put 2∏ in front of integral Fifth step – plug in boundary limits dx – use x intercepts, dy – use y intercepts Sixth step – multiply Radius and Height Seventh step – plug dx or dy

Example