Unit Seven: Apps of Integrals Flashcards
How do you find the area between two curves using x-bounds?
Area of curve on top minus area of curve below (x limits where they intersect)
How do you find the area between two curves using y-bounds?
Area of curve to the right minus area of curve to the left (y limits where they intersect)
What is the base formula for the disk method?
The integration of pie*r^2 from a to b where r is y when revolved around a horizontal axis and x when revolved around a vertical axis
Rectangles are perpendicular to the axis of revolution
When is the washer method used?
Large figure area minus small figure area when both can be found using the disk method
What are the base dimensions of the rectangle used in the shell method for revolution about horizontal and vertical lines?
2pieradius * height
Horizontal-
2piey * x
Vertical-
2piex * y
Rectangle is always parallel to the axis of rotation
What is the total distance traveled?
The integration from first x to second x of the absolute value of the velocity function
What is position shift?
The integration from first x to second x of the velocity function
How does speed relate to velocity?
Speed is the absolute value of velocity, where -velocity is backward and +velocity is forward
When is speed increasing?
When velocity and acceleration have the same sign
When is speed decreasing?
When velocity and acceleration have different signs
When does a change in direction occur?
When velocity is equal to 0
How do you find the arc length of Y=f(x) or X=g(y)?
Integration from value to value of the square root of 1 plus the derivative squared
When do you use dy or dx for disk/shell for vertical/horizontal axis?
Dy for vertical disk or horizontal shell
Dx for horizontal disk or vertical shell
