1. Application of Integrals Flashcards

2. Washer Method

3. Washer Method is used to find the volume between two curves that are rotated about the x-axis or the y-axis. The method involves integrating the area of the cross-sections which is a circle without a center. The formula for either rotation is basically With y-axis rotation, f(x) in the formula represents the function furthest right and g(x) represents the inner function (aka the one furthest left). With x-axis rotation, f(x) represents the function that is on top while g(x) represents the function that is closer to the x-axis (the bottom function). The cross-section

4. Inverse Area Method

5. The inverse method is used to find the area between two curves when it is difficult to use the x-axis method or the y-axis method. This method requires that the functions be rewritten in inverse form ( so you switch the x’s& y’sand solve to isolate y). Graph out the new equations. Then you take the integral of the curve on top minus the curve on bottom on interval.

6. Shell Method

7. The Shell Method is also used to find the volume of a function or between two functions rotated around an axis or a line. The tricky part with this method is that it switches the variable of integration. So if you’re rotating about the x-axis then the shell method is written with the equations using y and vice versa. The formula for shell method is The variable r represents the radius of the shell which is just the simple variable of integration either x or y depending on the problem. Unless its rotated around a line then it’s a number minus the x/y. The h represents the height of the shell which is the function itself. If you’re finding the area between two functions around then h represents the function on top minus the function on bottom. The w represents the thickness of the shell which is just dx or dy.

8. Which method of rectangular approximation does this this graph use?

9. Left Rectangular Approximation LRAM

10. Disk Method

11. Disk Method is used to find the volume of a single function rotated about either the y-axis of the x-axis. Once a function is rotated about an axis we can take the integral of it’s cross-section to find the volume. The cross-section of a single function rotated would be a circle. So to find the volume, this formula is used