# Calc II Review



## Applications of Integration



Areas between curves:

![This figure is a graph in the first quadrant. There are two curves on the graph. The higher curve is labeled “f(x)” and the lower curve is labeled “g(x)”. There are two boundaries on the x-axis labeled a and b. There is shaded area between the two curves bounded by lines at x=a and x=b.](https://openstax.org/apps/archive/20220801.182716/resources/6887bfb9acfdd744947bda1fc671dabe2a7e8f62)

![This figure has three graphs. The first graph has two curves, one over the other. In between the curves is a rectangle. The top of the rectangle is on the upper curve labeled “f(x*)” and the bottom of the rectangle is on the lower curve and labeled “g(x*)”. The second graph, labeled “(a)”, has two curves on the graph. The higher curve is labeled “f(x)” and the lower curve is labeled “g(x)”. There are two boundaries on the x-axis labeled a and b. There is shaded area between the two curves bounded by lines at x=a and x=b. The third graph, labeled “(b)” has two curves one over the other. The first curve is labeled “f(x*)” and the lower curve is labeled “g(x*)”. There is a shaded rectangle between the two. The width of the rectangle is labeled as “delta x”.](https://openstax.org/apps/archive/20220801.182716/resources/5f4e87f76cbea27bec02b2fdf6869ac1e517b60a)

![image-20220831002055484](/home/zack/.config/Typora/typora-user-images/image-20220831002055484.png)



## Solids of revolution

![image-20220831002525079](/home/zack/.config/Typora/typora-user-images/image-20220831002525079.png)

![image-20220831002428715](/home/zack/.config/Typora/typora-user-images/image-20220831002428715.png)

![image-20220831002544709](/home/zack/.config/Typora/typora-user-images/image-20220831002544709.png)



## Disk Method



![image-20220831002700927](/home/zack/.config/Typora/typora-user-images/image-20220831002700927.png)

![image-20220831002709670](/home/zack/.config/Typora/typora-user-images/image-20220831002709670.png)

![image-20220831002730242](/home/zack/.config/Typora/typora-user-images/image-20220831002730242.png)



## Shell Method



![image-20220831002759836](/home/zack/.config/Typora/typora-user-images/image-20220831002759836.png)

![image-20220831002816085](/home/zack/.config/Typora/typora-user-images/image-20220831002816085.png)

![image-20220831002847120](/home/zack/.config/Typora/typora-user-images/image-20220831002847120.png)

![image-20220831003233094](/home/zack/.config/Typora/typora-user-images/image-20220831003233094.png)

![image-20220831003242865](/home/zack/.config/Typora/typora-user-images/image-20220831003242865.png)



## Cylindrical Shells



![image-20220831003340109](/home/zack/.config/Typora/typora-user-images/image-20220831003340109.png)

![image-20220831003410212](/home/zack/.config/Typora/typora-user-images/image-20220831003410212.png)

![image-20220831003432839](/home/zack/.config/Typora/typora-user-images/image-20220831003432839.png)

![image-20220831003508810](/home/zack/.config/Typora/typora-user-images/image-20220831003508810.png)

![image-20220831003519716](/home/zack/.config/Typora/typora-user-images/image-20220831003519716.png)



![image-20220831003541215](/home/zack/.config/Typora/typora-user-images/image-20220831003541215.png)

![image-20220831003548497](/home/zack/.config/Typora/typora-user-images/image-20220831003548497.png)



## Arc Length



![image-20220831003728910](/home/zack/.config/Typora/typora-user-images/image-20220831003728910.png)



![image-20220831003710836](/home/zack/.config/Typora/typora-user-images/image-20220831003710836.png)



![image-20220831003720935](/home/zack/.config/Typora/typora-user-images/image-20220831003720935.png)

![image-20220831003752859](/home/zack/.config/Typora/typora-user-images/image-20220831003752859.png)



## Mass from density

Mass = density times length.

![image-20220831003821932](/home/zack/.config/Typora/typora-user-images/image-20220831003821932.png)



## Center of mass



![image-20220831004217034](/home/zack/.config/Typora/typora-user-images/image-20220831004217034.png)